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FARADAY DISCUSSIONS OF THE CHEMICAL SOCIETY NO 65 1978 Colloid Stability This Faraday Discussion incorporates The First Rideal Lecture, given by Professor J. Th. G. Overbeek, and commemorates the lifelong contributions to Interfacial Science of E. K. Rideal THE FARADAY DIVISION CHEMICAL SOCIETY LONDONISBN: 0 85186 978 5 lSSN : 0301 -7249 0 The Chemical Society and Contributors 1978 Printed in Great Britain by Richard Clay (The Chaucer Press), Ltd., Bungay, SuffolkA GENERAL DISCUSSION ON Colloid Stability llth, 12th and 13th April, 1978 A GENERAL DISCUSSION on Colloid Stability was held at Lunteren in The Netherland; on the 1 lth, 12th and 13th April, 1978. Dr. G. D. Parfitt introduced Professor J. Th G. Overbeek, who delivered the First Rideal Lecture in the presence of the Presiden of the Faraday Division, Professor F.C. Tompkins, F.R.S., and about 260 Fellow: and guests. Among visitors to The Netherlands were: Dr. S. C. Agarwal, Switzerland Mr. A. P. Allen, U.K. Mr. B. R. Alves, U.K. Dr. R. Aveyard, U.K. Dr. P. Bagchi, U.S.A. Dr. F. Balestrazzi, Italy Mr. R. C. Ball, U.K. Mr. M. Barker, U.K. Dr. G. T. Barnes, U.K. Mr. K. Barnett, U.K. Dr. R. Beckett, Australia Dr. L. Benjamin, U.S.A. Dr. K. H. Berneis, Switzerland Dr. D. F. Billett, U.K. Mr. W. Black, U.K. Dr. A. Bleier, U.S.A. Mr. K. Bridger, U.K. Dr. R. Buscall, U.K. Dr. B. J. Carroll, U.K. Mr. D. J. Cebula, U.K. Mr. R. Cheesman, U.K. Dr. A. H. Chojnicki, U.K. Miss J. Clarke, U.K. Dr. D. R. Cooper, U.K. Dr. W. D. Cooper, U.K. Dr. T. Corner, U.K. Dr. D. F. Darling, U.K. Dr.E. Dickenson, U.K. Dr. D. Distler, West Germany Mr. A. Doroszkowski, U.K. Dr. F. Dumont, Belgium Mr. G. A. Dunn, U.K. Dr. A. E. Durno, U.K. Dr. D. Eagland, U.K. Mr. L. Eriksson, Sweden Dr. D. Fairhurst, U.K. Prof. G. H. Findenegg, West Germarty Mrs. Y . A. Fish, U.K. Mr. L. R. Fisher, Australia Dr. R . R. Ford, U.K. Dr. Y . Gilliams, Belgium Dr. A. R. Goodall, U.K. Dr. J. W. Goodwin, U.K. Dr. J. W. S. Goosens, West Germany Dr. D. E. Graham, U.K. Mr. P. A. Grandjean, Switzerland Mrs. M. J. Grant, U.K. Prof. P. Gray, U.K. Mr. M. Grimson, U.K. Dr. A. Grubenmann, Switzerland Mr. F. Griiner, West Germany Dr. M. L. Hair, Canada Dr. W. Haller, West Germany Mr. H. R. Harper, U.K. Dr. R. Harrop, U.K. Prof. T. W. Healy, Australia Dr. W. Hess, West Germany Prof.G. J. Hills, U.K. Dr. J. A. Hockey, U.K. Dr. R. Horn, France Dr. D. B. Hough, U.K. Dr. R. G. Hughes, Belgium Dr. W. Hunsmann, West Germany Dr. J. N. Israelachvili, Airstralia Dr. A. D. James, U.K. Dr. M. J. Jaycock, U.K. Dr. F. Jones, U.K. Dr. I. S. Jones, U.K. Dr. A. M. Joseph-Petit, Belgium Dr. F. Jost, West Germany Dr. N. Kallag, Yugoslavia Dr. K. J. Kayem, U.K. Dr. J. B. Kayes, U.K. Dr. I. W. Kellawag, U.K. Prof. E. Killmann, West Germany Dr. J. Klein, Israel Dr. I. KrznariC, Yugoslavitr Mr. R. Lambe, U.K. Dr. R. G. Laughlin, U.S.A. Mr. E. J. Lawson, U.K. Mr. J. C. Le Bell, Finland Dr. W. Lehmann, West Germany Prof. H. N. W. Lekkerkerker, Belgiiim Dr. H. Lervik, Sweden Dr. S . Levine, U.K. Dr. A. Lips, U.K. Dr. P. Luner, U S A . Dr. R. L. 5. Lyster, U.K. Dr.A. J. G. Maroto, Argentina Dr. R. S . Marsden, U.K. Dr. C. J. Martin, U.K. Dr. G. E. Martin, U.K. Mr. R. Martin Speirs, U.K. Dr. R. Menold, West Germany Prof. J. Mewis, Belgium Dr. R. J. L. Miller, U.K.iv A GENERAL DISCUSSION Dr. S. A. Mitchell, U.K. Dr. B. Nazir, U.K. Dr. E. L. Neustadter, U.K. Mr. D. W. J. Osmond, U.K. Prof. R. H. Ottewill, U.K. Dr. J. F. Padday, U.K. Dr. G. D. Parfitt, U.K. Mr. R. M. Pashley, U.K. Mr. A. R. Pitt, U.K. Dr. M. Plaisance, France Prof. A. Posner, Australia Dr. J. E. Proust, France Dr. M. Pyrlik, West Germany Dr. J . H. Raistrick, U.K. Dr. J. D. F. Ramsay, U.K. Dr. D. G. Rance, U.K. Dr. K. J. Randle, U.K. Mr. D. Rawlins, U.K. Dr. P. Richmond, U.K. Dr. J. Rigler, West Germany Dr. I. D. Robb, U.K. Mr. B. Roberts, U.K. Dr. P.Rutter, U.K. Dr. H. Sato, Japan Dr. H. Schliiter, West Germany Dr. G. Schreier, West Germany Dr. S . Shaya, U.S.A. Dr. I. Sheiham, U.K. Dr. P. Sherman, U.K. Prof. A. Silberberg, Israel Dr. P. Sinclair, U.K. Dr. A. L. Smith, U.K. Dr. J. B. Smitham, U.K. Dr. I. Snook, Australia Prof. H. Sonntag, East Germany Dr. J. F. Stageman, U.K. Dr. E. Staples, U.K. Dr. P. Stenius, Sweden Mr. H. D. Stone, U.K. Dr. Stone Masui, BeZgium Prof. S . P. Stoylov, BuZgaria Dr. G. Szasz, Switzerland Dr. Th. F. Tadros, U.K. Dr. C. Taupin, France Dr. B. Tavernier, BeZgium Mr. S . Tavernier, Belgium Dr. G. Taylor, U.K. Prof. F. C. Tompkins, U.K. Dr. U. Tuerck, West Germany Dr. K . Turban, West Germany Dr. T. G. M. van de Ven, Canada Dr. W. J . van Megen, Australia Dr. B. R. Vijayendran, U.S.A.Dr. B. Vincent, U.K. Mr. F. A Waite, U.K. Dr. T. Walker, U.S.A. Dr. A. J. I. Ward, Ireland Prof. A. Watillon, BeIgium Dr. J. Wegner, West Germany Dr. W. Wenzel, West Germany Dr. J . W. White, France Prof. S . G. Whittington, Canada Dr. R. Wicke, West Germany Dr. G. R. Wiese, U.K. Dr. G. Winter, West Germany Mr. A. J . Wishart, U.K. Dr. P. Woditsch, West Germany Mr. K. Wojak, West Germany Dr. C. J. Wright, U.K. Dr. C. A. Young, U.K. Dr. D. A. Young, U.K.CONTENTS Page 7 20 25 33 43 58 65 76 92 101 114 146 156 164 175 194 202 215 230 The First Rideal Lecture: Microemulsions, A Field at the Border Between Lyophobic and Lyophikc Colloids by J. Th. G. Overbeek Measurement of Forces between Surfaces Immersed in Electrolyte Solutions by J. N . Israelachvili Polymer-stabilized Free Liquid Films by J. Lyklema and T.van Vliet Direct Measurements of the Interaction between Adsorbed Macromolecular Layers by F. W. Cain, R. H. Ottewill and J. B. Smitham GENERAL DISCUSSION Mechanical Spectroscopy of Colloidal Dispersions by J . Mewis and G. Schoukens Structure and Stability of Concentrated Boehmite Sols by J. D. F. Ramsay, S. R. Daish and C. J. Wright Neutron Scattering from Colloids by D. Cebula, R. K. Thomas, N. M. Harris, J. Tabony and J. W. White Statistical Mechanical Approach to Phase Transitions in Colloids by W. van Megen and I. Snook Application of Modern Concepts in Liquid State Theory to Concentrated Particle Dispersions by A. Vrij, E. A. Nieuwenhuis, H. M. Fijnaut and W. G. M. Agterof GENERAL DISCUSSION On Coagulation in the Primary Minimum by G.Frens Coagulation of Amphoteric Latex Colloids: Reversibility aptd Specipc Ion Eflects by T. W. Healy, A. Homola, R. 0. James and R. J. Hunter On Enzymatic Clotting Processes. Part 3.-Flocculation Rate Constants of Paracasein and Fibrin by T. A. J. Payens GENERAL DISCUSSION Macromolecular Surfaces Phases and the Stability of Colloidal Dispersions by A. Silberberg Modes of Polymer Adsorption with Excluded Volume on Parallel Colloidal Plates and their Interactions by S. Levine, M. M. Thomlinson and K. Robinson GENERAL DISCUSSION Preparation and Stability of Novel Polymer Colloids in a Range of Simple Liquids by D. H. Everett and J. F. StagemanCON TENTS Magnetic Birefringence as a Tool for Determining Adsorbed Polymer Layer Thicknesses by P. C. Scholten Efect of Molecular Architecture of Long Chain Fatty Acids on the Disper- sion Properties of Titanium Dioxide in Non-aqueous Liquids by A. Doroszkowski and R. Lambourne Influence of Adsorbed Proteins on the Stability of Polystyrene Latex Part ides by A. van der Scheer, M. A. Tanke and C. A. Smolders Concentration Eflects in Polymer Flocculation and Stabilization by D. S. Duckworth, A. Lips and E. J. Staples Equilibrium Aspects of Heteroflocculation in Mixed Sterically-stabilized Dispersions by B. Vincent, C. A. Young and Th. F. Tadros Some New Aspects of and Conclusions on Theory of Stability of Colloids and their Experimental Verification by B. V . Derjaguin GENERAL DISCUSSION vi 242 252 264 288 296 306 313 342 INDEX OF NAMES

ISSN:0301-7249    

DOI:10.1039/DC97865FP001

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

THE FIRST RIDEAL LECTURE Microemulsions, A Field at the Border Between Lyophobic and Lyophilic Colloids BY J. TH. G. OVERBEEK* Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachussetts, 021 39 U.S.A. Received 17th May, 1978 Microemulsions can be regarded as thermodynamically stable dispersions of droplets of one phase in another phase. There are continuous transitions to swollen micelles, when the droplets become ex- tremely small, and to coarse emulsions when the droplets are large. The mechanism leading to the formation of microemulsions is the tendency to extend the interfacial area until the concentrations of surfactants are sufficiently low that non-negative interfacial tension is achieved. The role of the combination of a surfactant and a cosurfactant is seen in their leading to a decrease in the interfacial tension to potentially negative values.An expression is given for the Gibbs energy of the whole sys- tem, for the special case of an ionized surfactant and a non-ionized cosurfactant. The minimization of this Gibbs energy leads to the stability conditions for the microemulsion. The factors which pro- mote O/W and W/O emulsions, respectively, are briefly discussed. The electrical contribution to the interfacial tension depends on the particle size. This leads to a narrow size distribution. It is finally pointed out that, in principle, fine dispersions of solids in a liquid may be thermodynamically stable in the presence of large amounts of easily adsorbed compounds. 1 . INTRODUCTION This lecture is given to honour the memory of Sir Eric K.Rideal. I felt that it would not be adequate for me to give a review on some older subject, but that I would be expected to offer something completely new or at least to offer a new look at some older problem. I have chosen this last approach. I shall talk to you about systems lying on the borderline (one might say: forming the interface) between lyophobic and lyophilic colloids and more specifically about microemulsions. Microemulsions are mixtures of water and “ oil ” (e.g., toluene or cyclohexane) made transparent and apparently homogeneous by the presence of a fairly large amount of surfactant, or more usually of a surfactant and a cosurfactant. Their spontaneous formation and long lasting stability indicate that they are thermodynamically stable and not only stable in the kinetic sense. They have found several practical applica- tions and have attracted a great deal of attention in recent years on account of their use in tertiary oil recovery and as examples of (nearly) isodisperse suspensions of spherical particles. Vrij’s presentation on “ Application of modern concepts in liquid state theory to concentrated particle dispersions ” in the present meeting is an * Permanent address: Van’t Hoff Laboratory, University of Utrecht, Padualaan 8, Utrecht, The Netherlands.8 MICROEMULSIONS example of the use of the last named property.Much literature on microemulsions is available, including a recent book, edited by L. M. Prince,2 but notwithstanding all the work done on these systems since their introduction by Hoar and Schulman3 in the early forties, our understanding of their properties still has many gaps.In this lecture I will not be able to fill these gaps, but I will try to analyse why these dispersed systems are stable, whether and how extensively they differ from ordinary emulsions and from micellar solutions and how we might understand their isodispersity. Finally I want to discuss briefly the possibility that other, especially solid in liquid, dispersions may be thermodynamically stable. 2. MICROEMULSIONS Microemulsions may be described as small droplets (diameter 5-50 nm) of a liquid (I) dispersed in another liquid (11) by virtue of the presence of a fairly large concentra- tion (e.g., 20%) of a suitable combination of surfactants. It is then obvious, as shown schematically in fig.1, that, at least in principle, there are continuous transitions to micellar systems having some liquid (I), solubilized in the micelles and to coarse emulsions (diameter 500 nm and above) on the other hand. In this discussion I shall direct my attention primarily to systems in which the drop- lets are large enough (Le., diameter > 5 nm) to bring their centre and its immediate surroundings out of the range of short range interactions with the surfactants in the interface. Without denying the importance of microemulsions stabilized by non- \ A 0.7nm B 3nm 30 nm 300 nm 0 C D FIG. l.-Schematic representation of water droplets of various radii (0.7 to 300 nm) in oil with an ionized surfactant at the interface.A may be considered as a water swollen micelle. D comes in the size range of ordinary emulsion droplets. B and C are typical microemulsion droplets. The number of surfactant ions in the surface, s, and in the bulk, s', per particle when the surfaoe excess is about 1 ion per 0.5 nmz and the bulk concentration about 0.001 mol dm is listed. A B C D S 12 225 22 500 2.25 x lo6 St 0.001 0.1 70 70 OOOJ . T H . G. OVERBEEK 9 ionic surfactants, I shall assume in this talk that the main surfactant is ionic as in the original cases reported by Schulman. A fairly typical composition is: 33% (by weight) water, 34% toluene, 23% potassium oleate and 10% hexanol, which forms W/O microemulsions with a droplet diameter of about 8 nm. The main questions presenting themselves then are : (1) What is the significance of the combination of two surfactants, one highly polar (ionic) and one morc lipophilic (the alcohol)? (2) How can the thermodynamic stability and the spontaneous formation be explained ? (3) What determines whether an OlW or a W/O emulsion is formed? (4) How isodisperse are these systems? (5) Can similar systems be made with dispersed solids? 3 .INTERFACIAL TENSION AND ADSORPTION Schulman4 in his later papers postulates that the main feature of microemulsions was a zero interfacial tension between the two phases, or rather a negative interfacial tension at the original composition of the two phases which would lead to a spon- taneous extension of the interface and adsorption of surfactant until the remaining concentration of surfactant had become so low that the interfacial tension would rise to zero or to a positive value.This aspect explains the necessity of using two rather different surfactants. Aqueous solutions of surfactants such as K-oleate generally show a dependence of surface tension or interfacial tension, 7, as sketched in fig. 2. At low concentrations the surfactant is adsorbed at the air-water and at the oil- water interface and the surface (or interfacial) tension starts to decrease. Even before the surface tension has decreased very much the (y, log c) curve achieves a steep, nearly constant slope, indicating that the adsorption is saturated. The Gibbs isotherm, eqn (3.1) gives the relation between y, the amount adsorbed per unit area, Ti, and the chemical potential pi of component, i, cm.c .log c FIG. 2.-Showing how a combination of two surfactants may lower the interfacial tension to zero and to potentially negative values. The drawn line gives the interfacial tension for a surfactant with a c.m.c. The dotted lines refer to the same surfactant, but used after the interfacial tension has been lowered by a cosurfactant. The two dotted curves refer to slightly different affinities of the surfactant for the interface covered with cosurfactant.10 MICROEMULSIONS where ai is the activity of i and cf its concentration. The factor 2 in the denominator arises from the dissociation of the ionic surfactant. For a nonionic surfactant and also for an ionic surfactant in the presence of an excess of a nonsurface active electrolyte, the factor 2 drops out. The decrease in y with increasing c stops rather suddenly at the critical micelle Concentration (c.m.c.).Above this concentration any further addition of surfactant is used to form micelles and although ci still increases, ai remains nearly constant. As Wagne~,~ among others, has pointed out, it is not an unfortunate accident that the concentration at which the interface is saturated and the c.m.c. are close together. The surroundings of a detergent ion or molecule at a saturated interface and in a micelle are rather similar. Consequently, their standard free energies are nearly equal and they are formed at nearly the same concentration of single molecules, so that it is rarely possible to reach zero or potentially negative interfacial tension with only one surfactant. However, the effects of more than one surfactant may be cumulative, as follows directly from surface thermodynamics.The differential of the Gibbs energy, dG, may be written dG = -SdT + Vdp + ydA + Epfdni ( 3 4 where A is the area of the interface and other symbols have their usual meaning. Adding d(pini) for one component (either the surfactant or the cosurfactant) to both sides we derive easily : ($) T,p, all nj except ni,A T,p,pi, all n, except nd (3.3) = -f t. Using eqn (3.3) first for the cosurfactant, (i = co) and then for the surfactant (i =sa) (or the other way around) we have We see from eqn (3.4) that upon addition of the second surfactant the interfacial tension will decrease further, the essential requirement being a not too small adsorp- tion of the second surfactant.Whether it replaces the first surfactant or is absorbed in addition to it is immaterial, just as it is not essential for the two surfactants to form a surface complex. If the two surfactants are of the same type, e.g., both water soluble anionic surf- actants, they will form mixed micelles and this will lower the activity of the second surfactant added and decrease both its r and dp. But if they are rather different in nature, e.g., one mostly water soluble and the other mostly oil soluble, they will only slightly affect each other’s activity and their combined effect on the interfacial tension may be large enough to bring the interfacial tension down to zero and potentially below zero at finite concentrations.4. CONSEQUENCES OF ZERO INTERFACIAL TENSION When the conditions for negative interfacial tension are reached, the interface will expand, adsorbing both surfactants in the proczss until their activities are lowered to such values that y = 0. As a rule this implies that the remaining concentration of the ionic surfactant is below the c.m.c., since above the c.m.c. its activity is nearlyconstant.J . TH. G . OVERBEEK 11 Then all but a small fraction of this surfactant is in the interface and thus the inter- facial area is equal to the amount of this surfactant times its molar area (in the presence of the co-surfactant). The molar area is of the order of 0.5 nm2 X NAv. In certain combinations of amounts of the various components the large total interfacial area involved might be arranged in lamellar form, these systems showing the properties of liquid crystals.At other concentrations typical low viscosity, isotropic transparent microemulsions are found, the huge interfacial area being com- prised of the surfaces of a large number of very small droplets. One might wonder why, at y = 0, these droplets are spherical, as there seems to be no driving force to bring such a droplet to the shape of minimum area. However, a microemulsion droplet contains most of its soap ions in the surface and very few in the bulk. Even a small deformation will increase the surface area with a concomitant decrease in adsorption density. A compensation of this decrease by further adsorp- tion from the bulk would lead to a rather large decrease in the bulk concentration and to a strong rise in the interfacial tension, which would drive the shape back to spherical.We may consider this as a manifestation of the Gibbs-Marangoni effect. It also explains why microemulsion droplets behave to a good approximation as hard spheres.6 The situation y = 0 would be determined by the composition of the two bulk phases and that of the interface, the last named one being controlled by the composi- tion of the bulk phases. These conditions are expected to be at most only slightly dependent on the droplet size. Therefore, when stable microemulsions can be ob- tained, macroemulsions may also be thermodynamically stable, provided the com- position of the bulk phases is the same as in the microemulsions.Such macroemulsions would not appear to be different from ordinary kinetically stabilized emulsions : they would be turbid, they would cream or sediment, but they would not coalesce, since that would decrease the interfacial area and make the interfacial tension negative. The fairly high concentration of alcohol or other co- surfactant in the oil phase might, of course, be a drawback for practical applications. One difference between such macroemulsions and the corresponding microemul- sions might be that the van der Waals attraction between the droplets would be stronger in the macroemulsions, possibly leading to local coalescence in W/O emulsions, so as to invert them into O/W emulsions. These, by virtue of the longer range of the electro- static repulsion, would then be thermodynamically and kinetically stable.5 . GIBBS ENERGY OF THE SYSTEM The condition y = 0 is not sufficient to describe and understand microemulsions, however important it may be to expIain the driving force towards their formation. For thermodynamic stability the Gibbs energy of the total system must achieve a minimum value. This Gibbs energy contains several terms as discussed by Rucken- stein and Chi.' We follow the same line of thought, although our treatment is rather different in its details from that in ref. (7). The first contribution to the Gibbs energy of a microemulsion, AG1, refers to the Gibbs energy of mixing of surfactant and water and of cosurfactant and oil. To keep our equations reasonably simple, we shall assume that the mutual solubilities of water and oil, of the surfactant in oil and of the cosurfactant in water are negligible. Thus we have12 MICROEMULSIONS The primes refer to the final situation in which most of the surfactant (TSaA) and a great portion of the cosurfactant (TcoA) have disappeared from the solutions into the inter- face.The original amounts of surfactant and cosurfactant are n,, and nco, respec- tively. The second term, AG2, refers to the interfacial area and is AGz = Yfinal A + (nsa - n'sa)p'sa + (nco - n'co)~'co. (5.2) We split yfinal, the final interfacial tension which is close to zero, into Yuncharged, the interfacial tension that would obtain if no electrical double layer had been formed, at otherwise unchanged compositions of solutions and interface, and an electrical term Jyoda, where yo is the surface potential and CT the surface charge density.ra Splitting yflnal into these two contributions is useful since Tuncharged presumably is based on short range effects and thus to a first approximation independent of the curvature of the interface, whereas the electrical term encompasses long range effects and is therefore a function of the radius, a, of the particles. Finally, there is a second free energy of mixing term, AG,, due to the mixing of the droplets (say of water) into the continuous phase (oil). We are dealing with concen- trated emulsions and thus we have to take non-ideal behaviour into account. Vrij et aL6 have shown that the Percus-Yevick8-Carnahan-Starling9 approximation for hard spheres applies rather well to the light scattering of oil continuous microemulsions.We have therefore applied the same theory, starting with the equation for the osmotic pressure, l7, of a hard sphere suspension in the form where v h , is the molar volume of the hard spheres and p their volume fraction. tion and phs by integration. The final result for AG3 is : From n we derive p (dispersion medium), then dphs using the Gibbs-Duhem rela- In p - 1 + p ~ 4 - 3 ~ + ~ & ) . (1 - PI2 vhs (5.5) The detailed calculation is given in the appendix. individual components is then: The total Gibbs energy of the microemulsion, leaving out the standard terms for the At equilibrium dG must be zero and d2G positive. To a first approximation A , nrsa = Ylsa - r s a A , and dc0 = nco - rcoA are variable, ?uncharged depends on nlsa and dc0, nhs can be related to A , but Sy/,da depends on rsa which we may assume to be constant in the region of saturation adsorption and depends only slightly on a which itself is proportional to A - l .J .TH. G. OVERBEEK 13 (Iil) where the relation nhs NAv = A3/36n(nwVw)2 has been used to eliminate q , S * (111) is zero according to the Gibbs adsorption isotherm. Consequently, The terms (I) and (11) are zero on account of the Gibbs-Duhem relation and 4 - 3p dG = dA [?uncharged + IWOda + 1271(n,vw)2 + In ")1 vhs The three terms are rather unequal in magnitude. The last term is always negative. It can be transformed by using A - nsa/rsa and for a rather high ratio of soap to water, nSa/n, = 0.04 (corresponding to a mass ratio of about 0.7) and p = 0.5, it has the value -0.2 dyn cm-l.For p = 0.1 the value would be -0.5 dyn cm-l, and tp would have to be below to make this term equal to -1.0 dyn cm'l. The electrical Gibbs energy per unit area of the double layer is quite high at the high charge densities involved, so high that no simple theory will give a precise value. If it is assumed that most of the energy is present in a molecular condenser (Stern- layer) with a capacity of 15pF cm-2 (order of magnitude found at a mercury-water interface) then at a charge density of 1 elementary charge per 0.5 nm2, Jyoda becomes I 0 2 2 capac. (5.9) $Yy,da = - - - - 340 dyn cm-l and the corresponding potential difference would be 2.1 V. Such a large potential would certainly force a large fraction of the counterions in between the charged heads of the ionic surfactant and decrease the effective charge density to between 50% to 10% of its value, thus reducing the potential to several hundred mV and the (positive) contribution to the interfacial tension to 50 dyn cm-l or less. This still requires to have a high negative value in order to reach dG = 0. The conclusion so far must be that in a microemulsion the interfacial tension, including the electrical term has very low, but slightly positive values.The small variations in the total interfacial tension required to balance variations in the free energy of mixing (osmotic) term can be easily obtained by small variations in nfsa, and n',,, leading to variations in Yuncharged. 6. OIL-IN-WATER OR WATER-IN-OIL So far it has not been necessary to specify whether an O/W or a W/O microemul- sion was the stable one.Several factors are playing a role here. The osmotic term increases with increasing p and thus favours the situation in which the phase with the smaller volume fraction forms the droplets, with in addition a small advantage for the oil phase to form the droplets because V,,, > Vwater.14 MICROEMULSIONS For W/O emulsions the hard sphere volume is only slightly larger [see ref. (6)] than the water volume, since the hydrocarbon tails of the surfactant may interpenetrate to a certain extent, when two droplets come close together. For O/W emulsions, on the other hand, the repulsion between double layers may easily have a range of several times l/lc ( 1 / ~ = Debye length), and unless the electro- lyte concentration (other than the ionized surfactant) is very high, it would increase the hard sphere radius by 5 nrn or more.This factor works in favour of the W/O emul- sion, especially for small droplets. Furthermore, establishing a curvature of the adsorbed layer at a given adsorption will be easier with water as the droplet phase, since in this case the hydrocarbon tails of the surfactant will have more freedom to move around than when they are inside the drop. Consequently, other things being equal the interfacial tension will be slightly lower for W/O than for O/W emulsions. It has been mentioned earlier that van der Waals forces would work in favour of O/W emulsions, but only when the droplets are large. A unique preference does not exist, but on the whole W/O emulsions will be fav- oured with small drops, O/W with large drops.However, since the difference in stability between the two possible forms is not large, small specific effects such as packing of the interfacial layer and the volume fraction may become decisive factors. 7 . DROPLET SIZE DISTRIBUTION Finally, we arrive at the issue of the isodispersity. If at a given total interfacial area the particles all have the same size, that size is determined by the following two equations (for a W/O emulsion). 4nnh,a2NA, = A and 47E - nh,a3NA, = n,V, 3 where we neglect for simplicity the term dSaVsa in the total volume of the droplets. solving these equations for a and nhs leads to and nhs = A3/36nNAy(n, Vw)2.a=- 3nJw A (7.3) However, the same area and the same volume can be obtained with a particle size distribution about the above radius. The kind of distribution and its width will de- pend on the differences in Gibbs energy amongst the particles of different sizes. Transfer of water or surfactant from one droplet to other droplets (keeping the total area, the total volume and nfsa constant) does not change the total Gibbs energy. Neither would a moderate deviation from isodispersity change the osmotic term, since it is mainly determined by p, which stays constant and nhs, which changes little. Also Yuncharged remains the same, but now the secondary effects of the particle radius on the electric term become important. The radial dependence of the standard Gibbs energy per particle, E(a), is then As mentioned above, there is no completely satisfactory way of estimating the elec- trical free energy for these very highly charged double layers, but we may assume thatJ .TH. G . OVERBEEK 15 starting at some distance from the surface the double layer behaves as if it emanated from a lower surface charge density, e.g., from 1 elementary charge per 200 A2 or 500 A2 (75 to 90% of the charge compensated very close to the head groups). When we consider the diffuse part of the double layer inside a spherical drop and assume as a first approximation that the Debye-Huckel linearization may be applied, then the potential I,Y would have to satisfy the equation with assuming that a concentration c of monovalent electrolytes is present.The solution of eqn (7.5) inside a spherical drop is (7.7) P sinh w w = with P equal to: a2r’F EEO(Ka cosh ica - sinh K a ) P = where I” is that portion of the surface charge density (in moles per unit area) that is not compensated very close to the surface. Levine and Robinson lo give a better approximation starting from the non-linear- ized Poisson-Boltzmann equation instead of from eqn (7.5), but it is more complicated. The main point in my discussion is to show the basic line of thought. In our linearized case the electrical contribution to the surface Gibbs energy is 1 a(r‘P)2 2~~,(ica coth Ka - 1) SWoda = Wsurf 0 = (7-9) For a certain value of a = a, the electrical term in eqn (7.4) just compensates ?“,,charged and therefore ?uncharged = -(SwOda)aO (7.10) Using now eqn (7.4), (7.10) and (7.9) we can write for E(a, + Aa) d E(a, + Aa) = 4na2 (Syoda)Aa = (7.11) where we have asumed that K a 3 1 so that we may approximate rca coth Ka - 1 = 7ca - 1 + 2 K-ae-2Ka + .. . (7.12) The particle size distribution function f ( a ) = dn,,/da is a Boltzmann distribution f (a) = dnhs/da = f (a,,) exp (- EfkT) = f (a,) exp (+ AaIAa,) (7.13) with Aa,, the width of the distribution equal to Aa, = ee,~~kT/2n(r’F)~ (7.14) which results in an exponential distribution with a sharp cut-off at the large particle size as sketched in fig. 3.16 MI CROE MU L S I ONS The distribution becomes narrower with decreasing IC (i.e., with decreasing electro- lyte concentration) and with increasing surface charge. Its width, expressed as Aa,, is independent of the average particle size.To give an idea of the numerical value of da,, we estimate it for a fairly high electrolyte concentration (0.1 mol d ~ n - ~ of a 1-1 electrolyte) and a surface charge density created by I" = 1 monovalent ion per 200 A2. Then Aa, is equal to da,[O.l mol dm-3 (1-1 electrolyte); l" = (NAv x 200 A")-'] = 0.7 A . (7.15) The conclusion is that the distribution is narrow, the narrower the lower the electrolyte concentration and the higher the surface charge. Although the calculation contains admittedly rather drastic approximations, the conclusion may be expected to hold also for more accurate calculations. ___)L a FIG. 3.-Particle size distribution function with a width da,. At the radius a,, the interfacial tension (yuncharpcd + Jyodv) is just zero [cf.eqn (7.10) and (7.1411. It was mentioned in the discussion after eqn (5.8) that the contribution of the inter- facial tension, ?uncharged + Jly,da, has to be slightly positive to counterbalance the free energy of mixing term. This will remain true for the particle size distribution described above, and in general will require the upper limit of the particle radius to be a1 < a,. The value a, and the number of droplets, NAv x nhs, are found easily from the distribution function, eqn (7.13), the total volume, n,Vw of the droplets and their total area, A . For a narrow size distribution (Aaw < Q ~ ) we have to a good approxim- ation (a> M 3n,Vw/A (7.17) n,, M A3/36nNAy(nw Vw)=. (7.18) The value a, - a, will depend on the volume fraction, p; a,, the radius at which the interfacial tension is exactly zero, adjusts itself by a small change in the free concentra- tions of the surfactants nlsa and dc0.Considering now the more general case, without the restriction that ua be large, we derive in the same way as eqn (7.1 1)J . TH. G . OVERBEEK 17 Aa d a( r'F)2 da 2&~~(rca coth Ka - 1) E(ao + Aa) = 4za2 - Aa 2n(r'F)21 - K2a2/sinh2 i a ~ ~ ~ r c ~ (coth rca - 1 /lca)2 2 ~ ( r ' F ) ~ =-- f (Ica)Aa, - _ - - &&OK2 (7.19) f(rca) has a very limited range, going from 1 for Ka + CQ via 2.018 for K a = 3 and 2.816 for K a = 1 to 3.0 for rca = 0. For small values of Ica, the distribution is nar- rower by as much as a factor 3 than that predicted by eqn (7.14). Qualitatively, the results obtained can be understood by noting that even a small microemulsion droplet contains several hundred surfactant ions.A relatively small change in the curvature of the surface leads to a small change in the convergence of the lines of force towards the centre of the (water) droplet and to a small change in the electrical Gibbs energy of the double layer per soap ion. The sum of hundreds of these small differences adds up to many times kT. It is also evident that the electrical free energy per unit charge in the surface is larger the smaller the droplet, if the double layer is inside the droplet. For an O/W emulsion the double layer would be outside the droplet, and thus the energy per unit charge would increase with increasing droplet size, leading to an exponential particle size distribution with a sharp cut-off at the small particle end.8. OTHER DISPERSIONS THAT ARE THERMODYNAMICALLY STABLE A few months ago Stol and de Bruyn," working on the nucleation and growth of oxides and hydroxides, remarked that it might be possible to obtain thermodynamic- ally stable dispersions of solids in cases in which the adsorption of potential determining ions is large enough to lead to a zero (or potentially negative) interfacial tension. If this could be realized systematically it might mean an important breakthrough in the preparation of stable dispersions. The idea need not be limited to potential determin- ing ions, since any additional positive adsorption, e.g., of surfactant ions or molecules would lead to a further decrease in the interfacial tension and increase the chances of obtaining thermodynainic stability.In looking for confirmation of this postulate, one need not expect spontaneous comminution, but it is conceivable that the growth of particles is stopped by this effect, and even " negative Ostwald ripening " might occur. Favourable conditions are : (a) a low interfacial tension to begin with, and thus preferably a low energy density solid rather than a high energy density one; (b) a very asymmetric point of zero charge, since this would favour high surface potentials; (c) strong adsorption of small molecules (or ions) so that r may become large. In " protecting " suspensions by this mechanism, small molecules are better than large, polymeric ones ; (d) use of more than one adsorbate; (e) a high electrolyte concentration is favourable in the case of potential determin- ing ions, since this would lead to a high charge density at a given surface potential; but if saturation adsorption of an ionic detergent is reached, then a low electrolyte concentration is preferable since this would give a high surface potential for the given surface charge.18 MI C ROEM U L SI 0 NS The remarkable stability of silica so1s12 at alkaline pH may be a case of this nature.9. CONCLUDING REMARKS The concept of potentially negative, but ultimately positive small interfacial tension explains the formation and thermodynamic stability of at least certain types of micro- emulsions and possibly other dispersions of solids. Isodispersity can be regarded as a consequence of the change in the electrical contribution to the surface tension with the curvature of the interface.A continuous transition from swollen micelles via typical transparent microemul- sions to macroemulsions is possible, although in the latter case the thermodynamic stability may be limited by the relatively stronger van der Waals interaction amongst the droplets. Refinement of the treatment as offered in this paper is possible and desirable. A search for other systems with this type of stability might be rewarding. In microemuIsions stabilized by a nonionic surfactant (cf. Shinoda and Friberg) l3 electrical effects as discussed in this paper are absent. Whether such systems are better characterized as swollen micelles or as dispersions of droplets with low interfacial tension is omitted from discussion here.I gratefully acknowledge constructive criticism by Prof. R. G. Donnelly of the text of this communication. APPENDIX DERIVATION OF EXPRESSION FOR THE GIBBS ENERGY OF MIXING OF HARD SPHERES I N A SOLVENT, EQN ( 5 . 5 ) The relation between the osmotic pressure, l7, and the chemical potential of the solvent, 1, is Pl = Pl* - nv1 (A.1) where V, is the molar volume of the solvent. (5.4) we have Using the value for n, given in eqn According to the Gibbs-Duhem relation dphs/dPl = -(I - (A.3) where x is the mole fraction of hard spheres. The mole fraction is expressed in the volume fraction, 9, by Then dphs can be writtenJ . TH. G . OVERBEEK 19 Integrating of the second term and combining the result with the first term we find: 2 3 Integrating eqn (A.6) from 9 = 0 to 9 leads to Since (x/p)&~ = Vl/vhs we finally have: The Gibbs energy of mixing can now be written Using V = nlVl + nhsvhs, Vln,P/vhs can be converted into in eqn (A.9) we obtain - q). Inserting this and this is the same as eqn (5.5). A. Vrij, E. A. Nieuwenhuis, H. M. Fijnaut and W. G. M. Agterof, Faruday Disc. Chem. Soc., 1978, 65, 101. Microemulsions, Theory and Practice, ed. L. M. Prince (Academic Press, New York, 1977). T. P. Hoar and J. H. Schulman, Nature, 1943,152, 102. J. H. Schulman and J. B. Montagne, Ann. N.Y. Acud. Sci., 1961, 92, 366; W. Stoeckenius, J. H. Schulman and L. M. Prince, Kolloid-Z., 1960,169, 170. C . Wagner, Colloid Polymer Sci., 1976, 254,400. W. G. M. Agterof, J. A. J. van Zomeren and A. Vrij, Chem. Phys. Letters, 1976,43,363. E. Ruckenstein and J. C. Chi, J.C.S. Faruday IZ, 1975,11, 1960. J. K. Percus and G. J. Yevick, Phys. Rev., 1958, 110, 1; E. Thiele, J. Chew. Phys., 1963,39, 474. N. F. Carnahan and K. E. Starling, J. Chem. Phys., 1969,51,635. lo S. Levine and K. Robinson, J. Phys. Chem., 1972, 76, 876. l1 R. Stol and P. L. de Bruyn, personal communication; R. Stol, Thesis (Utrecht, 1978). l2 R. K. Iler, The Colloid Chemistry ofsilica and Silicates (Cornell University Press, Ithaca, N.Y., l3 K. Shinoda and S. Friberg, Adv. Colloid Interface Sci., 1975,4,281. 1955), p. 91ff.

ISSN:0301-7249    

DOI:10.1039/DC9786500007

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Measurement of Forces between Surfaces Immersed in Electrolyte Solutions BY JACOB N. ISRAELACHVILI Research School of Physical Sciences and Research School of Biological Sciences, Institute of Advanced Studies, The Australian National University, Canberra, A.C.T. 2600, Australia Received 30th November, 1917 The forces between two mica surfaces immersed in various aqueous electrolyte solutions have been measured. From 200 nm down to contact separations four different types of force are operating. First, there are attractive van der Waals forces; these are non-retarded up to about 6.5 nm with a Hamaker constant of (2.2 f 0.3) x J. The van der Waals forces appear to be slightly stronger than expected from the Lifshitz theory. Second, there are repulsive double-layer forces. In lo-' mol dm-3 1 : 1,2 : 1 and 2 :2 electrolytes these are well accounted for by theory but at concentrations above mol dm-3 there are discrepancies with theory, especially for 2 : 1 electrolytes.Third, there are repulsive " hydration " forces; these decay exponentially with distance with the characteristic decay length of about 1 .O nm. Their magnitude varies from mica to mica and is largely independent of ionic strength. They are negligible at separations above 7.5 nm. Fourth, there are adhesion forces; these are complex and depend on a host of factors such as pH, type of electrolyte cations, mica orientation, etc., and are not simply given by extrapolating the long-range forces down to separations of the order of interatomic spacings. The forces measured are those between two crossed cylindrical sheets of molecu- larly smooth mica of radius R w 1 cm.The apparatus is similar to earlier models used for measuring the van der Waals force between mica surfaces in air and in vacuum,l the optical properties of liquid and monomolecular films,2 and in adhesion and boundary friction ~tudies.~ A short account of the experimental technique and some initial results were reported ear lie^.^ Forces may be measured to within &(3-5) x N, and distances to within k(O.1-0.2) nm. In general, the forces measured in dilute solutions were exponentially repulsive, whereas in more concen- trated solutions an attractive region (secondary minimum) often preceded the onset of repulsion. At very small separations, below about 5 nm, the repulsion often peaked (force barrier), below which the net force became attractive and resulted in the surfaces jumping into strong adhesive contact (primary minimum).The results show that at least four different, though not necessarily independent, types of force are operating between mica surfaces in aqueous solutions : van der Waals forces, double-layer forces, " hydration " forces and adhesive forces. These will be described and discussed in turn. EXPERIMENTAL RESULTS VAN DER WAALS FORCES The attractive van der Waals forces were studied in two ways. First, at high electrolyte concentrations, when double-layer repulsions are weak, the van der Waals forces may be measured in the region of a secondary minimum. Second, at small separations the surfaces often jump into molecular contact from a position, the forceJ .N. ISRAELACHVILI 21 barrier, where the repulsion is maximum. By noting the position and force at the jump an estimate may be made of the attractive force needed to bring about the jump into contact. Both methods require some extrapolation of the repulsive forces and between them provided information of the van der Waals forces in the range 1-1 5 nm. The van der Waals forces were found to be effectively non-retarded from -1 to -6.5 nm, with a Hamaker constant of A = (2.2 5 0.3) x J. Above 6.5 nm retardation effects set in and the forces decay more rapidly with increasing separation. The van der Waals forces were found to be largely independent of the type and concentration of electrolyte and of the strength and nature of the repulsive forces.Measurements of the refractive index of water and of aqueous solutions between two mica surfaces yielded values within 1% of bulk values for surface separations in the range 2-100 nm; we conclude that in theoretical calculations of van der Waals dispersion forces, the bulk refractive indices should be adequate for calculations of these forces down to separations of 2 nm. The following approximate expression, derived from the Lifshitz the or^,^ may be used to obtain a theoretical estimate of the dispersion force contribution to the non- retarded Hamaker constant : where n, = refractive index of water = 1.33, n2 = refractive index of mica = 1.60, and where oo = characteristic adsorption frequency for mica and water (which are the same) = 1.90 x 1OI6 rad s-,. Substituting these values into eqn (1) yields A,,,,.= 1.85 x 10”O J. A more detailed theoretical analysis has been carried out by Dr L. R. White, using a computer program to solve the Lifshitz equation as described earlierY6 who found that the non-retarded Hamaker constant is A N, 2.0 x J, but that retardation sets in at smaller separations than was observed. DOUBLE-LAYER FORCES In dilute KNOJ and NaCl solutions (lo4 - mol dm4), the measured double- layer repulsive forces are in remarkably good agreement with theory (i.e., exact solutions to the non-linear Poisson-Boltzmann equation) at separations ranging from five Debye lengths down to 0.2 Debye lengths. The interaction occurs at constant surface potential both as the surfaces approach each other and as the concentration is changed.The surface potential does not depend on the type of electrolyte (to 5 1 0 mV), and is weakly dependent on pH in the pH range 10-6, but falls rapidly at lower pH, reaching about a third of the high pH value at pH 3. The surface potential appears to be determined by the nature of the mica: micas of different chemical composition exhibited different potentials; these varied from 50 to 130 mV, but were usually between 70 and 100 mV, in the pH range 6 - 7. Lower potentials were associ- ated with a high K/Na ratio at the cleavage plane. In more concentrated 1 : 1 electrolyte solutions - 10-1 mol dnr3) the measured double-layer forces begin to deviate from theoretical expectations. The forces still decay exponentially with distance, but the exponential decay lengths are now x 20% higher than the theoretical Debye lengths.The surface potentials still remain con- stant, or fall slightly, at these higher concentrations. In dilute solutions of 2: 1 electrolytes Ca(NO,),, CaCl,, MgC1, and BaC1, the double-layer forces are much reduced from those in 1 : 1 electrolytes at the same con- centration (the surface potentials in 2: 1 electrolytes are smaller than those in 1 : 1 electrolytes, and the interaction appears to be intermediate between constant charge22 FORCES BETWEEN SURFACES IN ELECTROLYTES and constant potential). In mol dm-3 solutions the forces are in fairly good agreement with exact solutions of the Poisson-Boltzmann equation in the range 5 - 0.3 Debye lengths; but in mol dmm3 solutions the forces decay faster with distance than expected from theory; the mean exponential decay lengths being 20 - 45% lower than the theoretical Debye lengths.At concentrations of mol dm-3 and above, the double-layer forces for 2:l electrolytes were too weak to be accurately measured. In one experiment with the 2:2 electrolyte MgS04 at mol dm-3, the double-layer forces were in good agreement with theory. We conclude that the behaviour of symmetric 1 :1 electrolytes is well described by the Poisson-Boltzmann equation, but that asymmetric 2 : 1 electrolytes are not well described by the Poisson-Boltzmann equation already at concentrations as low as IW3 rnol dm-3. The Outer Helmholtz Plane (OHP), i.e., the plane where the diffuse double-layer starts, is not necessarily at the mica-water interface but may be as far as 2.5 nm beyond this interface.As two mica surfaces are brought towards each other for the first time in a given solution, the OHPs are irreversibly shifted towards the mica surfaces. The shifts commence once the surfaces are sufficiently close together (closer than -10 nm), and there are indications that the shifts occur at a constant pressure (between two flat surfaces, calculated according to the Deryaguin approxi- mation)’ of -lo4 N r r 2 , or 4 . 1 atmospheres. These irreversible shifts of the OHPs lead to hysteresis effects in that the repulsive forces appear to be reduced after the first approach. Similar effects have been known to occur in swelling pressure studies on clay sheets, notably between montmorillonite sheets in water and NaCl so1utions.8-10 Our results indicate that such hysteresis effects are real and not a bothersome artifact due to the forced alignment of edges or non-parallel sheets on the first compression, as has been suggested.Our results may further be interpreted as furnishing evidence that a structured aqueous region exists near a mica surface (whose refractive index is nevertheless very close to that of bulk water). This region may extend as far as 2.5 nm beyond each surface with the OHP located at its outer bound- ary. Beyond this there is little or no structuring, the dielectric constant of water is now very close to the bulk value of E = 80, and diffuse double-layer theory holds [any significant deviation of e from 80 would have shown up in the slopes of the (double- layer force, distance) curves].When two mica surfaces are forced to approach each other the shifts of the OHPs probably reflect the progressive breakdown of the struc- tured aqueous regions as the surfaces come together. Hysteresis effects were rarely ob- served in dilute mol dm-3 solutions, and they could be brought about by increasing the electrolyte concentration. The existence and extent of hysteresis varied from mica to mica, and it therefore depends on the nature of the mica in addition to that of the electrolyte. Our observations are not inconsistent with the many “ anomalous ” surface and colloidal properties of clay mineral, silica and other oxide “HYDRATION” FORCES Apart from the normal van der Waals and double-layer forces, there is also an additional long range repulsive force. The magnitude of this force varies from mica to mica; in all cases where it was large enough to be accurately measurable it was found to be roughly exponential in the range 1.0-6.0 nm with a characteristic decay length of about 1 .O nm.This force is largely independent of the electrolyte concentra- tion, the pH and the mutual crystallographic orientation of the two mica surfaces. It appears to depend mainly on the nature of the mica and, to a lesser extent, on the cations present in the solution. The effectiveness of this third force depends on theJ . N. ISRAELACHVILI 23 strength of the van der Waals and double-layer forces, but it is negligible at separations above 7.5 nm.At low electrolyte concentrations, when double-layer forces are strong, its influence may be negligible right down to the force barrier which is de- termined solely by the DLVO forces. At high electrolyte concentrations, when double-layer forces are weak, this force may determine the position and depth of the secondary minimum as well as that of the force barrier. It is probably due to this force that silica dispersions are sometimes stable at very high ion strengths and undergo reversible coagulation. Our findings are consistent with those of Olejnik and White19 who measured the self-diffusion of water in thin layers between clay mineral surfaces of vermiculite and montmorillonite, and found that in the range 0.5-6.0 nm this decayed exponentially away from the surface with a characteristic decay length of -1 .O nm.* Hunter and Leyemdekkers22 found a similar exponential decay length ( -1.1 nm) for the viscosity of water between clay mineral surfaces. Further, a number of other unrelated experimental and theoretical (empirical) studies on water23 have also indicated an exponential " coherence length " for bonding in liquid water of z 1 nm. We conclude that (i) hydration forces exist, and that their effective range may extend to surface separations of -7.5 or -4 nm beyond each surface; (ii) there appear to be at least two different types of hydration force, characterised by different exponential decay lengths [see also ref. (24)], and (iii) more generally, any deviations from bulk values of such liquid properties as the self-diffusion, viscosity, molecular mobility, etc., near surfaces appears to be accompanied by a force between two such surfaces (this has recently been substantiated on theoretical grounds by MarEelja and coworkers in their theoretical analyses of " structural " force^).^^-^' ADHESION FORCES Previous studies of adhering mica surfaces using multiple beam interferometry have yielded valuable information on the fundamental mechanisms underlying adhesion and f r i ~ t i o n .~ ~ ~ ~ - ~ ~ The advantage of using multiple beam interference fringes is that both the shapes of the contacting surfaces and their separation may be accurately monitored. The theory of the adhesion of deformable solids is in dispute. According to the theory of Johnson et aZ.31r28 the pull-off force (adhesive force) at which two adhering surfaces come apart, P, is related to the adhesion energy per unit area, y, by P = 3nRy, (2) where R is the radius of curvature of the surfaces, which may be equated with the radius of the curved mica surfaces used in our experiments.The radius of the contact zone at pull-off rp is finite and is related to the contact radius under zero external force ro by According to the theory of Deryaguin et aZ.32 the pull-off force is P = 4nRy, and rp = 0, i.e., the surfaces come apart when the contact radius has fallen to zero. Our results show that at pull-off the contact radius is always finite, and that for pull-off in air rJr0 = 0.56 & 0.05, while in aqueous solutions rp/ro = 0.64 0.10. These * A similar study of the diffusion of water between ammonium perfluoro-octanoate bilayers20 yielded a characteristic decay length of 0.2 nm. This result is particularly interesting in view of some recent measurements of the forces between lecithin bilayers in water," where an exponentially decaying hydration force was measured at separations below 2 nm with a characteristic decay length of 0.19 nm.rp/ro = (1/4)'13 = 0.63. (3)24 FORCES BETWEEN SURFACES IN ELECTROLYTES results support the conclusions of Taborz8 that the Johnson theory gives a better description of adhesion than the Deryaguin theory. However, both theories predict that y cc P cc r;, and while we did observe that larger contact radii ro were accom- panied by larger pull-off forces P, a dependence of the form P cc r,3 was not obtained.Eqn (2) allows us to determine the adhesion energy y from the pull-off force P and the radius R, which are easily measurable. The range of values we have obtained for adhesion energies y in aqueous electrolyte solutions were enormous, ranging from -10 mJ rnm2 (erg cm-2) to below 0.01 mJ-2. The adhesion energies in KN03 andNaCl solutions increased markedly with decreasing pH even though the van der Waals forces, the double-layer forces and the hydration forces were comparatively insensitive to pH changes. The adhesion energies were also found to depend greatly on the type of cation present (i.e., cation specific), as well as on the mutual crystallographic orientation of the two mica surfaces. Our results, therefore, show that the adhesive forces of mica surfaces in contact in a primary minimum are complex, and not simply given by extrapolating the van der Waals, double-layer and hydration forces to separations of the order of interatomic spacings.I am indebted to G. E. Adams and R. K. Tandon for their excellent research assistance. D. Tabor and R. H. S . Winterton, Proc. Roy. SOC. A, 1969,312, 435; J . N. Israelachvili and D. Tabor, Nature, 1972,236, 106; Proc. Roy. SOC. A, 1972,331,19. J. N. Israelachvili, Nature, 1971, 229, 85; J . Colloid Interface Sci., 1973, 44, 259. J. N. Israelachvili and D. Tabor, Nature, 1973, 241, 112; Wear, 1973,24, 386. J. N. Israelachvili and G. E. Adams, Nature, 1976,262, 774; also J.C.S. Farahy I, 1978, 74, 975. J. N. Israelachvili and D. Tabor, Prog. Surface Membrane Sci., 1973,7, 1.L. R. White, J. N. Israelachvili and B. W. Ninham, J.C.S. Farahy I, 1976,72, 2526. B. V. Derjaguin, Kolloid-Z., 1934,69, 155. Harrington and R. H. Ottewill, Kolloid-Z., 1972, 250, 655. I. C. Callaghan and R. H. Ottewill, Faraday Disc. Chem. SOC., 1974, 57, 110. lo K. Norrish and J. A. Raussell-Colom, Clays and Clay Minerals, 1963, 10, 123. l1 Y. G. B6rube and P. L. de Bruyn, J. Colloid Interface Sci., 1968,28, 92. lZ J. T. Webb, P. D. Bhatnagar and D. G. Williams, J. Colloid Interface Sci., 1974, 49, 346. l3 P. D. Bhatnagar, Colloid Interface Sci., ed. M . Kerker (Academic Press, N.Y., 1976), vol. IV, a L. M. Barclay and R. H. Ottewill, Special Disc. Faraday Soc., 1970,1, 138; L. M. Barclay, A. p. 225. J. P. Quirk, Israel J. Chem., 1968,6,213. l5 W. D. Kemper and J. P. Quirk, Proc. Soil Sci., SOC. Amer., 1970,34, 347. l6 A. M. Posner and J. P. Quirk, Proc. Roy. SOC. A, 1964,278,35. l7 B. V. Deryaguin and N. V. Churaev, J. Colloid Interface Sci., 1974,49, 249. la W . Drost-Hansen, J. Colloid Interface Sci., 1977,58, 251. l9 S. Olejnik and J. W. White, Nature, (Phys. Sci.), 1972, 236, 15. J. B. Hayter, A. M. Hecht, J. W. White and G. J. T. Tiddy, Faraday Disc. Chern. SOC., 1974, 57, 130. 21 D. M. LeNeveu, R. P. Rand, V. A. Parsegian and D. Gingell, Biophys. J , 1977,18,209; Nature, 1976,2!59,601. 22 R. J. Hunter and J. V. Leyemdekkers, J.C.S. Farahy I, 1978,74, 450. 23 N. H. Fletcher, Rep. Prog. Phys., 1971,34,913; J. Cryst. Growth, 1975,28, 375. 24 K. J. Packer, Phil. Trans. B, 1977, 278, 59 (especially section 5c). 25 S. Mar&lja and N. RadiC, Chem. Phys. Letters, 1976, 42, 129. z7 S . MarEelja, Biochim. Biophys. Acta, 1976,455, 1. 28 D. Tabor, J. Colloid Interface Sci., 1977, 58, 2. 29 A. I. Bailey and J. S . Courtney-Pratt, Proc. Roy. SOC. A, 1955,227, 500. 30 A. I. Bailey and S . M. Kay, Proc. Roy. Sac. A, 1967,301,47. 31 K. L. Johnson, K. Kendall and A. D. Roberts, Proc. Roy. Sac. A, 1971,324,301. 32 B. V. Deryaguin, V. M. Muller and Y. P. Toporov, J. Colloid Interface Sci., 1975,53, 314. S. MarEelja, D. J. Mitchell, B. W. Ninham and M. J. Sculley, J.C.S. Faraday II, 1977,73,630.

ISSN:0301-7249    

DOI:10.1039/DC9786500020

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Polymer-stabilized Free Liquid Films BY J. LYKLEMA AND T. VAN VLIET Laboratory for Physical and Colloid Chemistry of the Agricultural University, De Dreijen 6, Wageningen, The Netherlands Received 12th December, 1977 The equilibrium thicknesses and drainage have been measured of free liquid films, stabilized only by poly(vinylalcoho1) (PVA) or partially esterifled poly(methacry1ic acid)(PMA-pe). The equilibrium thickness of PVA-films considerably exceeds twice the ellipsometric or the hydrodynamic thickness of one adsorbed layer. This is attributed to the dominant steric repulsion of isolated tails, a conclu- sion that is substantiated by theoretical arguments. The change in drainage behaviour of PMA-pe films as a function of pH correlates well with the conformational transition that this polyelectrolyte undergoes in the bulk and in the adsorbed state.Thin liquid films are familiar models for studying colloid stability. Their equili- brium thickness is determined by the same forces governing lyophobic sol stability. In particular, soap films have been used as a tool to study double layer repulsion and van der Waals attracti0n.l” By the same token, polymer-stabilized free liquid films (henceforth abbreviated as polymer films) can be used to study the interaction between adsorbed polymer layers and hence may be regarded as a tool for measuring the force of steric stabilization. This force is not so easy to obtain. Two examples involving dispersed systems are provided by Doroszkowski and Lamboume4 and by Cairns et ul. Publications on polymer films are particularly scanty: Musselwhite et aL6m7 and Graham and Phillipss reported on protein-stabilized films and Sonntagg gave a preliminary report on thickness measurements of aqueous poly(vinylalcoho1) (PVA) films between oil droplets.The scarcity of such contributions reflects the experi- mental difficulties rather than meagre scientific interest of these systems. Below, we describe equilibrium thickness measurements of PVA-films and a few preliminary experiments on films stabilized by the polyelectrolyte PMA-pe [a co- polymer of poly(methacry1ic acid) and its methyl ester]. The PVA-films permit a force-balance analysis. Since these films are rather thick, dispersion forces play a relatively minor role. As double layer repulsion is absent, the equilibrium thickness is determined by steric repulsion and hydrostatic pressure only, allowing the evaluation of the former.Subsequent analysis in terms of a theory of steric stabilization gives information on the distribution of polymer segments over loops and tails, a piece of information that is not readily obtainable otherwise. EXPERIMENTAL METHODS Film drainage and equilibrium thickness measurements have been made on small hori- zontal films, i,n an apparatus which, apart from some modifications, was identical to that used by Agterof and Vrij at Utrecht,lo who in turn based their construction on ideas by Sheludkom2 Films were formed in a glass ring, inside diameter 3.7 mm and width 3.0 mm. The film diameter varied between 1.5 and 3.0 mm depending on the disjoining pressure. Hydrostatic suction could be controlled between 0 and 10 mm water by raising or lowering a containerwith polymer solution, which was connected to the film.The temperature was 25.00 5 0.02 "C. Thicknesses were obtained using the reflection of light. The light source was a Spectro- physics model 155 0.5 mW He-Ne laser, operating at a wavelength of 632.8 nm. The incident light was attenuated by a factor of 100. Photodiodes were Hewlett Packard PIN diodes (5082-4204). The intensity of the reflected light beam was corrected for fluctuations in the laser beam intensity by taking the ratio of the two intensities. Using a chopper and filtering out only that part of the measured signal with the same frequency as that of a second reference signal derived from the chopper, measurements could be performed in daylight.Details of this technique have been given by van Vliet.ll The polymer films were formed by raising the container, placing a droplet of solution in the glass ring, then lowering the container just far enough for the liquid layer in the ring to remain too thick to form a film. At this stage a waiting time of 1 h, except where other- wise stated, was observed. This waiting time is a characteristic variable for polymeric films since macromolecular adsorption is known to be a relatively slow process. Film thicknesses h were determined from the intensity ratio Irb/Irs of the reflected light from the film to that of a silvery film, (that is: a film for which I, is at its first maximum), using the familiar expression Irh I I,, (I + Y ~ ) ~ sin2 A (1- r2)2 + 4r2 sin2 A - _ where Y is the Fresnel coefficient = (nf - no)/(nf + no); nf and no are indexes of refraction of the film material and vacuum respectively, and 2nnfh cos cc 20 A = if cc is the angle of refraction, measured inside the film and lo is the wavelength in vacuum of the light used.Eqn (1) gives the so-called equivalent water thickness, assuming the films to be optically homogeneous water films (nf =n,). However, polymer films have obviously an index of refraction which depends on position in the fiIm, for which a correction must be applied. For an assembly of parallel sheaths of differing thicknesses and differing indices of refraction, Frankel and Mysels have formulated the correction factor.12 Polymer films can be considered as a limiting case with n changing continually.Van Vliet has shown'l that with respect to refraction this situation may to a good approximation be replaced by a block distribution, so that the form of the correction term Ah becomes qualitatively identical to that for classical soap films with no = 1 : However, quantitatively the thickness hl of the equivalent polymer layer exceeds the corres- ponding thickness of a soap film, whereas the index of refraction of this layer, nl, exceeds n, by only a small amount, much less than in the case of a soap film. For nf, the index of refraction of the core, we chose the index of the corresponding bulk solution. The amount of polymer I-',, per surface layer and the thickness of this layer were deter- mined ellipsometrically by Mr.Benjamins and Dr. de Feyter of Unilever Research Vlaard- ingen, Netherlands. The values of n1 and hl were obtained, assuming dn/dc to be a constant for a given polymer. This constant, in turn, was determined in an Abbe refractometer. The low polymer concentration in the heart of the film permitted one to consider the Fresnel coefficient as being independent of h." MATERIALS Two PVA-samples (205 and 2107) were commercial products from Kuraray, Japan; sample PVA-R2 was kindly supplied by Dr. Scholtens of our laboratory. Some characteris- tics are collected in table 1. The M-distribution is rather broad and probably of the Flory- type.13*14 Details of the viscometric molecular weight average determination are given in ref.(1 1); the conformational parameters (r2>*- and o! were obtained, using @ = 2.1 x 1021J . LYKLEMA AND T . VAN VLJET 27 in the Stockmeyer-Fixman eq~ati0n.l~ In order to suppress evaporation the PVA-film measurements were done in 1 mol dm-3 glycerol, which, at least in other cases has been shown to have no measurable effect on h.l0 In 1 mol dmh3 glycerol both (r2>* and a are a few percent lower than in water. TABLE 1 .-CHARACTERISTIC PARAMETERS OF PVA-SAMPLES. r.m.s., end-to- degree of end distance nature of Ac- sample hydrolysis ah. (r")"/nm a distribution 205 88 f 1 42500 20.2 1.06 blocky 21 7 88 f 1 143000 39.2 1.12 blocky R-2 83.4 f 1 149000 35.3 random The PMA-pe sample was manufactured by Rohm AG, Darmstadt, FRG, and available under the trade name Rohagit S, low viscosity grade.Its properties have been described.16 For this polyelectrolyte - lo5; the fraction of ester groups is 0.32, probably random. RESULTS AND DISCUSSION PVA-FILMS Fig. 1 displays equilibrium thicknesses measured under various conditions. These thicknesses are corrected for optical inhomogeneity; Ah in eqn (3) amounted to -2.0 to -3.7 nm, depending on the nature of the PVA. In this figure, each plotted point represents an entirely new experiment, i.e., it applies to a different film, made from a new drop of polymer solution in the ring. Consequently, the uncertainty bars denote the compounded error of inadvertent alterations in the procedure, waiting regime, drainage behaviour, etc., and may be considered as indicative of the absolute accuracy.The effect of waiting time, i.e., the effect of aging of the polymer solution surface prior to film formation, was absent within experimental error for waiting times between 2 min and 2 h, see the inverted (apex down) triangles in the PVA 205, 400 p.p.m. curve. Comparison of the 400 and 4000 p.p.m. curves for PVA 205 shows that a tenfold increase in concentration leads only to a few percent increase in h. The satisfactory accuracy in combination with very good reproducibility, if a given film is measured at several pressures, are strong indications that the stationary states observed are genuinely equilibrium films, that is, films for which the sum of all forces is zero. Below they will be treated in this way. The effects of A4 and the nature of the film material are quite pronounced.An increase in M by about a factor of 3 leads to an increase in h by several tens of a percent. Random PVA R2 gives thinner films than the corresponding blocky sample of the same M, PVA 217; moreover, the random sample is relatively more susceptible to pressure changes. This may be related to the lower adsorption of this particular sample (table 2). The remarkably high equilibrium thicknesses deserve special attention. Table 2 collects other characteristic thicknesses of the PVA samples. The value (hz)* = 0.68 hellips. is the r.m.s. layer thickness according to McCrackin and C o l ~ o n , ~ ~ assuming the decrease in the index of refraction with distance from the surface to be exponential. Obviously, h(P, -+ 0) exceeds twice the thicknesses reported in table 2 by at least a factor of 2.Such thick PVA films have been independently found by Sonntagg (al- though in his case dh/dP, is less) and by Onda in our laboratory.28 FREE POLYMER FILMS 100 90 80 Ec -. .c 70 60 5c 1," \ PVA R2 Y "\ \ 1 PVA 217 I f \ 1 1- 20 LO 60 P, I N m-* FIG. 1 .-Equilibrium thicknesses of PVA-films as a function of hydrostatic pressure. Bulk con- centration 4000 p.p.m. except where otherwise stated. V-Experiments with variable waiting time. In explaining the great difference between h(P,+O) on the one hand and lzellips. and <r2)* (see table 1) on the other, it must be realized that the three techniques involved in measuring these three values '' see " different phenomena: h in films is a measure of the steric repulsion force between two adsorbed polymer layers, helllps.is based on an index of refraction contrast between the adsorbed polymer and the solution and (r2)* is related to the extent of drainage through a polymer coil. The very high values of h in films are in our view due to a few long tails present in the adsorbed sheaths. Such tails would be almost invisible in ellipsometry and probably TABLE 2.-ELLIPSOMETRIC DATA OF ADSORBED LAYERS OF PVA. sample c0nc.lp.p.m. he,l*ps/nm ( h2}*/nm rplmg m-2 PVA-205 400 PVA-205 4Ooo PVA-217 4Ooo PVA-R-2 4000 17 11.6 3.1 21 14.3 3 . 2 29 19.8 3.7 18 12.3 2.0J . LYKLEMA A N D T . V A N VLIET 29 80 exert little effect in increasing the hydrodynamic coil radius in solution. However, their presence is strongly felt by a second polymer layer. If this picture is correct, the equilibrium thicknesses of fig.1 virtually reflect the steric repulsion of terminally- anchored, isolated tails. A rigorous quantitative elaboration of this picture is not yet possible because many of the relevant data are not available. For instance, we do not know how long the tails are, how many there are per polymer molecule, nor what their length distribu- tion is. Even so, the following semiquantitative analysis may be helpful. First, irrespective of any specific model, it is always possible to compute the force of steric repulsion F' for these films from the balance F. + Fh + Fw = 0, where Fh is - -4 I A I 1 1 I " 50 60 70 80 90 h inm FIG. 2.-Cteric repulsion in PVA-stabilized films. Bulk concentration 4000 p.p.m.except where otherwise stated. the hydrostatic force and Fw the van der Waals force, in our case calculated with a Hamaker constant of 4.4 x J, correcting for retardation in the same way as Lyklema and Myse1s.l Fig. 2 gives the results. Integration of these curves produces the interaction energy." Such figures can be useful for testing theories of steric interaction. Below, we undertake a semiquantitative interpretation, based on the consideration that tails dominate the repulsion. For equal tails, Hesselink et aZ.18 derived for the increase in free energy due to volume restriction of an assembly of average tails AV,, = 2 vkTW(i,h) (4) where i i s the average number of segments in a tail and v is the number of tails per unit area. The function W(i,h) is tabulated.18 The corresponding osmotic contri- bution, due to the overlap of polymer layers is formulated by the same authors as 3 1 2 ( ~ 2 - 1)kTv2 (r2)M(i,h) (5)30 FREE POLYMER FILMS where a is the linear expansion parameter.Table of M(i,h) values are available. The quantitative problem is that all tails are not equally long; moreover, it is not known how many there are. At any rate, the tail length distribution obviously depends on the dispersity of the polymer in the adsorbed state. In order to obtain this distribution, we have assumed that it equals the bulk distribution, which is probably of the Flory or " most probable " type, i.e., f ( M ) = TABLE 3 .-NUMBER OF ADSORBED POLYMER MOLECULES IN THE VARIOUS MOLECULAR WEIGHT FRACTIONS weight number of polymer molecules range of M this range PVA 205 PVA 217 fraction in (x 10-15/m-2 )adsorbed in this range 0-M 0.632 57.3 M-2M 0.233 21.1 2M-3M 0.0855 7.75 3M4M 0.03 15 2.85 4M-5M 0.01 16 1.05 5M-00 0.0067 0.61 19.7 7.26 2.67 0.98 0.36 0.21 AMye-AN with y = 0 and A = A.13914 It is given in table 3.Using these data, the steric repulsion energy can be computed, if the number of tails per adsorbed molecule and the fraction X , of the polymer segments present in tails are chosen as adjustable parameters. Fig. 3 gives some characteristic examples. For lack of more detailed information, we assumed Xt to be constant in each M-fraction, this tends to over- estimate the slopes at lower h. However, given the approximations that had to be 14 12 10 E 7 ',& L r- 9 4 2 0 -2 PVA 205 0.60 I 2 PVA 217 0.3511 40 b I n m FIG.3.-Comparison of measured steric repulsion energies with model computations, based on interaction of isolated, terminally anchored tails. Each theoretical curve is indicated by a two- parameter code, the first representing the fraction of each polymer molecule available in tails, the second is the number of tails per adsorbed molecule. The van der Waals attraction is also given for comparison.J . LYKLEMA AND T . V A N VLIET 31 made, a reasonable fit between theory and experiment is obtained. In agreement with expectation, X,(PVA 217) < X , (PVA 205). If there is only one tail per molecule, lower values of X, are needed because in that case this single tail tends to be relatively long, that is: it would contribute relatively strongly to repulsion.The main point we wish to make is that these calculations confirm our conclusion that tails play a dominant role in the steric interaction in PVA-films. In due course our data will be used to test theories of steric repulsion. In connection with this study, recent calculations made by Mr. Scheutjens in our laboratory may be mentioned. This work is an extension of the lattice statistics of polymer adsorption by Di Marzio and Rubin,lg in that self-excluded volumes and polymer-solvent interactions are taken into account. It was found that although the fraction X , is usually to the lower side of the values required in our analysis, the lengths of the tails appear to be considerable, again supporting our main findings. Finally agreement is also obtained with theoretical work by Roe20 and Motomura et aL2’ POLYELECTROLYTE FILMS For PMA-pe in 0.05 mol dmV3 NaCl the drainage behaviour is less regular; firm data on equilibrium thicknesses have been obtained only in a few cases.The degree of neutralization a’ is a very important variable. At a‘ = 1 .O the films have a mobile character, they drain rapidly ( M 1 h), initially with a dimple, to iz - 120 nm, after which a slower thinning occurs till after 16-24 h an equilibrium is attained. For a’ z= 0.5 the films drained rapidly in the early stages, but below h z 100 nm drainage became very slow. For a’ = 0.1 the films are rigid and irregularities ensue; they are very stable. In this case we succeeded only twice in obtaining an equilibrium film with visually plane-parallel surfaces.The most interesting feature of this transition in drainage behaviour between mobile and rigid films with decreasing a’ is that it correlates well with the conforma- tional transition that PMA-pe undergoes in solution. We have shown that the transition occurs also in adsorbed PMA-pe layers and that it is reflected in the inter- action between adsorbed layers of this p~lyelectrolyte.~~*~~ There is also a correlation with the surface dilational modulus.11 In table 4 equilibrium thicknesses are compared with values obtained from TABLE 4.-THICKNESSES OF PMA-pe STABILIZED FILMS. CONCENTRATION 1000 P.P.m. ELECTROLYTE 0.05 mol d m 3 NaCl. a’ glycerol present h/nm h,llips.lnm 0.1 0.5 0.7 1 .o 45 f 20 12 50 f 10 25 60f 6 32 $1 3 15 (after 1 day) ellipsometric measurements.The trend of these exploratory data is that h exceeds 2hellips less than with PVA, which could mean that polyelectrolytes are less inclined to adsorb with long tails than are uncharged polymers. The authors thank Mr. Maasland and Mr. Wegh for their technical assistance and Drs. Van den Tempe1 and De Feyter of Unilever Research for constructive discussions,32 FREE POLYMER FILMS J. Lyklema and K. J. Mysels, J. Amer. Chem. SOC., 1965,87, 2539. A. Sheludko, Adv. Colloid Interface Sci., 1967, 1, 391. R. Aveyard and B. Vincent, Progr. Surface Sci., 1977, 8, 60. A. Doroszkowski and R. Lambourne, J. Colloid Interface Sci., 1973, 43, 97. 1976,54,45. P. R. Musselwhite and J. A. Kitchener, J. Colloid Interface Sci., 1967, 24, 80.' P. R. Musselwhite and J. Palmer, Proc. Vth Int. Congress Surface Active Substances (Barcelona, 1968, Ediciones Unidas), vol. 2, p. 505. D. E. Graham and M. C. Phillips, in Theory and Practice of Emulsion Technology, ed. A. L. Smith (Academic Press, London, 1976), p. 75. H. Sonntag, IV Int. Tagung iiber Grenzjlachenaktive Stofe (Akademie-Verlag, Berlin, 1977), p. 517. W. G. M. Agterof, Thesis (State Univ. of Utrecht, 1977). T. van Vliet, Meded. Landbouwhogeschool Wageningen, Netherlands, 1977, 77, 1. * R. J. R. Cairns, R. H. Ottewill, D. W. J. Osmond and I. Wagstaff, J. Colloid Interface Sci., l2 S. P. Frankel and K. J. Mysels, J. Appl. Phys., 1966,37, 3725. l3 J. G. Pritchard, PolyvinyZ Alcohol, Basic Properties and Uses, Polymer Monography Nr. 4 l4 B. J. R. Scholtens, Meded. Landbouwhogeschool, Wageningen, Netherlands, 1977, 77, 7. l5 W. H. Stockmeyer and M. Fixman, J. Polymer Sci., 1963, CI, 137. (Gordon and Breach, London, 1970). J. C. T. Bohm and J. Lyklema, in Theory and Practice of Emulsion Technology, ed. A. L. Smith (Academic Press, London, 1976), p. 23. F. L. McCrackin and J. P. Colson, in Ellipson7etry in the Measurement of Surface and Thin Films (Proc. Symp., Washington, 1963), ed. E. Passaglia, R. R. Stromberg and J. Kruger (Natl. Bur. Stand. Misc. Publ.), vol. 256, p. 61. F. Th. Hesselink, A. Vrii and J. Th. G. Overbeek, J. Phys. Chem., 1971,75, 2094. l9 E. A. DiMarzio and R. J. Rubin, J. Chem. Phys., 1971,55,4318. zo R. J. Roe, J. Chem. Phys., 1966, 44,4264. 21 K. Motomura and R. Matuura, J. Chem. Phys., 1969,50, 1281. 22 T. van Vliet and J. Lyklema, Proc. 1st Int. Conference on Surface and Colloid Science, ed. E. 23 T. van Vliet and J. Lyklema, J. Colloid Interface Sci., 1978, 63, 97. Wolfram (Budapest, 1975), vol. 1, p. 197.

ISSN:0301-7249    

DOI:10.1039/DC9786500025

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Direct Measurements of the Interaction between Adsorbed M acromolecular Layers BY FREDERICK w. GAIN,* RONALD H. OTTEWILL AND JAMES B. SMITHAM School of Chemistry, University of Bristol, Bristol BS8 ITS Received 28th December, 1977 Experimental methods have been developed for determining, as a function of their separation distance, the force of interaction between two macroscopic surfaces coated with adsorbed layers. The central element of the apparatus was two hemi-spherically capped silicone rubber cylinders. With the surfaces far apart, an aqueous solution of poly(viny1 alcohol) was placed between the caps to allow adsorption to occur. Under the influence of a normally applied pressure, the surfaces were forced together so that the liquid layer thinned and the adsorbed layers interacted.The rate of film thinning was measured by a reflectance technique and the distance of surface separation by multiple beam interferometry. The interaction pressure between the layers appeared to commence at a surface separation distance of 160 31: 20 nm and increased to about 1.5 x lo4 N m” at a distance of 70 nm. At shorter distances, the pressure rose steeply with decrease in distance and suggested the formation of a film with a high concentration of PVA between the surfaces. One of the principal ways of ensuring the stability of a colloidal dispersion is to coat the particle surfaces with a protective co1loid.l The latter is usually a macro- molecule; gelatin has frequently been used for this purpose. More recently the classical term “ protected colloids ” has been replaced by the term “ sterically stabil- ised ” dispersions. The latter name, in fact, first appears to have been used by Heller and Pugh2 to denote the fact that uncharged particles could be prevented from floc- culating by the addition of macromolecules.As pointed out by N a ~ p e r , ~ however, the term “ steric ’’ is used in this context with a broad thermodynamic connotation rather than with the restricted meaning its use has in organic chemistry. Knowledge of the forces which control steric stabilisation is still somewhat un- certain; evaluation of the force of steric repulsion as a function of the distance of separation between the surfaces has not yet reached the same quantitative experimental level as that achieved in the case of electrostatic and van der Waals forces, where direct measurements have been made using macroscopic surface^.^-^ In the case of steric stabilisation only a few direct attempts at measuring the forces have been made, one using a 2-dimensional compression at the oil-water i n t e r f a ~ e , ~ , ~ and others using a 3-dimensional compression method.l0-l2 One of the major developments in techniques for making direct measurements between macroscopic surfaces in liquids came with the work of Roberts and Tabor.4 These authors used an optically smooth spherical cap of transparent rubber, which was pressed against a flat glass surface in an electrolyte solution to give a thin liquid film between the glass and the rubber.The rubber deformed easily over local pro- trusions so that in the compression region, essentially parallel surfaces were formed with liquid between them.A more sensitive form of this apparatus was developed * Present address : Department of Chemical Engineering, University College of Swansea, Swansea SA2 8PP.34 ADSORBED LAYER INTERACTION in our laboratories5 and used to measure the pressure arising from electrostatic repul- sion as a function of the distance of surface separation. In this paper we describe our preliminary attempts to develop this technique in order to make direct measurements of the repulsive pressure developed between two surfaces with adsorbed polymer layers as these two surfaces approach to close dis- tances in the interactive region. The surfaces were essentially sterically stabilised by the adsorption of a polyvinyl alcohol-polyvinyl acetate copolymer from an aqueous solution.EXPERIMENTAL MATERIALS All water used was twice distilled from an all-Pyrex apparatus. The poly(vinylalcoho1)-poly(viny1acetate) copolymer (PVA) used was kindly supplied by Dr. T. Tadros, ICI, Plant Protection Division and was an Alcotex 88/10 originally made by Revertex Ltd. The poly(viny1acetate) content was 12% w/w and the weight average molecular weight determined by ultracentrifugation, was quoted as 45 000. A fractionation of the raw material by Dr. M. J. Garvey13 gave weight average molecular weights for the highest and lowest fractions as 67 000 and 8000 respectively. The cloud point in water was 52 "C. REFLECTANCE APPARATUS The principal part of the apparatus consisted of two silicone rubber cylinders with spherical caps submerged in a solution of PVA.The two rubbers A and B were mounted so that B was vertically above A as shown in fig. 1 . The rubber B was securely held by a clamp C so that it remained rigid during an experiment; this support was quite independent of the mechanism holding A. The latter was connected to the drive movement D of a micrometer unit (L. S . Starrett Co.). Lockable joints within the drive assembly allowed the spherical surface of the rubber to be both rotated around the drive axis and to be tilted. The micrometer drive, attached to a slotted beam, enabled movement of the rubber in the vertical direction to be obtained in a very precisely controlled manner. The base could be fixed in position using locking screws.The aqueous PVA solution was placed in the cup E with the spherical rubber surfaces maintained at such a distance that no distortion of the rubber occurred at zero applied pressure. A thin liquid film between the rubber surfaces was formed by driving the rubber A upwards using the drive unit D so that the rubber surfaces became distorted in the central region to a flat disc as shown in fig. l(b). Distortion of the rubber, as shown by changes in the Newton's rings, was observed through the eyepiece of the microscope G. In addition to a viewing eyepiece, the projector end of the microscope could be equipped with either a camera for photographing the films, or with a photomultiplier to monitor the intensity of light reflected from the film.PREPARATION OF THE RUBBER SURFACES These were prepared using Sylgard 184 resin kits as supplied by Dow Corning Ltd, Barry, Glamorgan ; the kits consisted of resin, methylvinylpolysiloxane and a curing agent, hydrogenmethylpolysiloxane. The resin and the curing agent were mixed together in the ratio of ten to one by weight. A metal cylinder was used as a mould and in the bottom of this was placed a plano-concave lens of focal length -3.6 cm with a diameter of 2.05 cm. After pouring the mixed resin and curing agent into the mould, the mixture was left until all the bubbles formed during mixing and pouring had disappeared. The mixture was then cured at 70°C for a period of 15 h. The silicone rubber cylinder, still with the lens attached,F . W. CAIN, R . H .OTTEWILL AND J . B . SMITHAM 35 E - n (a) ( b ) FIG. 1 .-(a) Schematic diagram of reflectance apparatus for measuring intereaction between adsorbed layers. A and B, silicone rubbers with spherical caps; C , clamp for rubber B; D, micrometer drive for movement of rubber A; E, cup for PVA solution; F, beam-splitter; G, microscope. (b) Dia- gram illustrating flattening of rubber surfaces under applied pressure. was then removed from the mould. The refractive index of the rubber, as determined by ellipsometry, was found to be 1.430 at a wavelength of 632.8 nm. Fuller and TaborI4 estimated the surface energy of the rubber as 40 mJ mW2 and the Young's modulus as 1.68 & 0.06 x lo6 N m-2. MULTIPLE BEAM INTERFEROMETRIC APPARATUS The basic lay-out of the multiple beam interferometric apparatus is shown in fig.2. The apparatus and arrangements for clamping the silicone rubbers remained as shown in fig. 1. However, for interferometry, white light was used as a source of illumination and the beam was passed through rubber lenses A and B at normal incidence uia a prism, P, mounted underneath the rubbers. The emergent ray was split by the beam splitter F, one portion passing into a viewing eyepiece G and the other portion being focused onto the slit of a Hilger and Watts D187 prism spectrograph. A major difference in this method of measurement was the preparation of silicone rubbers with a metal coating on the spherical surface. The initial procedure was exactly as described previously up to the point at which the lenses were removed from the mould.The rubbers were then mounted in pairs and silver deposited on to the spherical surfaces to give a silver film with a thickness of about 50 nm. A thin layer (= 5 pum) of poly(methylmethacry1ate) was then deposited on to the silver layer. This was carried out by evaporation of the solvent from dilute solutions of polymer using the method of Carnell.15 A 3.8% w/w solution of Perspex was prepared in redistilled acetone and placed inside a covered container. The silvered rubbers were mounted carefully in a cradle and lowered into the solution using a hand winch. After five minutes the rubbers were slowly raised and allowed to drain in a saturated acetone vapour atmosphere for a further 15 min. A cross-sectional view of the completed lens is shown in fig.2(b).36 ADSORBED LAYER INTERACTION H F G- f- $ f-- light ( a ) ( b ) FIG. 2 . 4 ~ 2 ) Schematic diagram of multiple beam interferometric apparatus for measuring inter- action between adsorbed layers. A and B, coated silicone rubbers; C, clamp for rubber B; D, micrometer drive for movement of rubber A; E, cup for PVA solution; F, beam-splitter; G, viewing eyepiece; €3, prism spectroscope; P, prism. (b) Cross-section of coated silicone rubber. T, poly- (methylmethacrylate) ; S, silver layer; R, silicone rubber. PROCEDURE FOR OBSERVATIONS ON THIN FILMS With the rubbers A and €3 in their respective holders (see fig. 1 and 2) the lower rubber was raised by the micrometer drive so that it was approximately 1 mm below the upper rubber. At this point both the rubbers were adjusted until the observed Newton's rings were concen- tric around the optic axis of the viewing microscope G.Rubber B was then tilted slightly until the reflection from its upper surface appeared in the field of view; it was then deliber- ately tilted through a small angle to ensure that the reflection moved out of the field of view. The centre of the Newton's rings was then rechecked for alignment and readjustment made if required. In the multiple beam apparatus tilting of the beam was not required. A contact area between the rubbers was then formed by moving the rubber A gently upwards. The contact area was accurately focused and the rubbers separated by a small distance. At this point a PVA solution was added to the cup. After allowing a period of time for adsorption equilibration to occur, rubber A was slowly advanced towards B so that a thin film was formed between the two surfaces.When the reflectance technique was used the reflected light intensity was observed with time as the liquid film drained to its equilibrium position. The film was taken to be at equilibrium when the reflected light intensity did not change for a period of at least 25 min. In the equilibrium position, the diameter of the film formed was determined using a graticule in the microscope eyepiece. The lower rubber was then moved upwards a small distance by the micrometer drive and a new position of equilibrium found at an increased applied pressure. In this way it was possible to obtain an estimate of the thickness of the liquid film as a function of the applied pressure.DETERMINATION OF FILM THICKNESS: (a) BY LIGHT REFLECTANCE MEASUREMENTS Light from a 2 mW helium-neon laser (wavelength = 632.8 nm) was directed on to the semi-silvered mirror F which was inclined at an angle of 45" to the horizontal (see fig. 1). Part of the light beam was transmitted by the mirror and was then baffled by a RayleighF. W. CAIN, R . H. OTTEWILL AND J . B . SMITHAM 37 horn whilst the reflected light was directed on to the thin liquid film between the rubbers. The light reflected back from the centre of the film passed into the microscope G and thence on to a photomultiplier. The current from the latter was converted into a voltage and output on a chart recorder in order to obtain a trace of the signal as a function of time. The reflected intensity was converted into a film thickness using the equation of Caballero.16 (b) BY MULTIPLE BEAM INTERFEROMETRY Interference of the incident beam of white light occurred in the thin sandwich, poly- (methylmethacrylate)-thin liquid film-poly(methylmethacry1ate) between the two silver layers as shown in fig.2. The emergent light after focusing onto the slit of a spectrograph pro- duced fringes of equal chromatic order (FEC0).17 The methods by which FECO can be used to measure the thickness of films sandwiched between silver-backed transparent sub- strates has been described in detail by Israelachvili.18 Initially, a contact area was formed between the rubber surfaces in the absence of polymer solution and the wavelengths of the FECO were obtained by comparison with a mercury reference spectrum.The contact was then broken, polymer solution added and a pressure applied as described previously. The shift in wavelength of the FECO for the odd order fringes enabled the total distance between the poly(methylmethacry1ate) surfaces to be calculated18 at each applied pressure. DETERMINATION OF THE FILM PRESSURE The change in contact area under a known applied load was measured independently using a beam apparatus of the type described by Lewis.lg This gave a calibration curve of average pressure against contact area. The thin film area was always measured in a com- pression experiment and the average pressure obtained from the calibration curve. The pressures quoted in this paper are average pressures and not Hertzian pressures.20 RESULTS REFLECTANCE MEASUREMENTS A typical curve of reflected intensity against time is shown in fig.3. This was obtained with an 0.2 g/100 cm3 solution of PVA between the rubber surfaces when subjected to an average pressure of 2 x lo4 N mW2. Rapid drainage between the surfaces occurred at this pressure but the first bright interference fringe which occurs at A0/4n, where Lo = wavelength of light in vacuo and n = the refractive index of the solution, is clearly visible. After the initial rapid drainage the intensity decreased gradually with time, passed through a minimum after about 10 min and then increased again. The minimum is illustrated in the expanded inset in fig. 3(a) and it can be observed that at this point the intensity became equal to the background and it thus corresponded to a point of zero reflectance.Since the condition for zero reflectance is that the refractive index of the film should be equal to that of the substrate, the minimum indicated that the refractive index of the solution phase had become equal to the refractive index of the silicone rubber, namely 1.430. Thus it was possible to calculate the concentration of PVA at this point from the relationship, where no = refractive index of water and dn/dc = the refractive index of PVA (taken as 0.160 cm3 g-1).21 This indicated that the concentration of PVA in the film was of the order of 0.55 g ~ m - ~ . Beyond the minimum point the intensity rose slightly and then became constant with time indicating that the liquid film had reached an equilibrium position at the38 ADSORBED LAYER INTERACTION pressure applied.It can also be inferred that in this position the PVA concentration was higher than 0.55 g ~ m - ~ . Although the reflectance measurements located the position of the minimum and hence established the polymer concentration in the film, it was not possible to calculate the thickness at this point since it corresponded to the position of zero reflectance. I I I I 1 I X, 12 14 16 18 20 t imel min 0 1 2 3 4 5 5 7 8 9 10 tirne/rnin FIG. 3.-Reflected intensity as a function of time for drainage of a 0.2 g/lOO cm4 PVA solution between silicone rubber surfaces. Inset : enlarged view showing minimum in reflected intensity ; --- , background intensity. However, an attempt was made to obtain an estimate of the total film thicknesses at the equilibrium positions using an optical sandwich model composed of, rubber- adsorbed layer-solution-adsorbed layer-rubber and the equation of Cabellero.16 Estimates of the adsorbed layer thickness made independently give values of the order of 40 nm.13*22 Hence, using this value and an adsorbed layer concentration of 0.55 g ~ m - ~ approximate values were obtained for the film thickness as a function of applied pressure.These are given in fig. 4. For comparison, a second curve is given assuming a much lower concentration in the adsorbed layer, i.e., 0.2 g ~ m - ~ . The different assumptions did not, in fact, alter the gradient of the pressure against dis- tance curve, but they did displace it laterally along the abscissa.It is, therefore, considered that these results do reflect the form of the curve. However, a difficulty exists with the reflectance method in that as a consequence of the very high concentra- tion of polymer in the thin film it was not possible to obtain a unique determination of film thickness without an independent determination of the film refractive index. Moreover, these data indicated that lower applied pressures were required in order to determine the initial steric stabilisation overlap region. MULTIPLE BEAM INTERFEROMETRIC MEASUREMENTS The multiple beam apparatus (see fig. 2) enabled the distance between the poly- (methylmethacrylate) surfaces to be obtained without assumptions being made about the adsorbed layer thickness and concentration and also allowed lower pressures to be applied. The results obtained with this apparatus are shown in fig.5. TheF. W. CAIN, R. H. OTTEWILI, AND J . B. SMIT€IAM 39 initial PVA solution used was 0.2 g/100 cm-3 and results were obtained with both water and 0.1 mol dm-3 sodium chloride solution as solvents for the PVA. The results obtained in the presence and absence of salt were identical, indicating that electrostatic interaction did not make a significant contribution to the interaction pressure. Compression-decompression experiments were also carried out and since the points fell on the same curve, it can be concluded that the interaction is a reversible one. 7 6 N 'E 5 '0 c 4 z \ * X $ 3 !! n 2 1 2- 20 40 60 80 100 b Inm FIG. 4.-Pressure against distance of surface separation, h, obtained from reflectance measurements using a 0.2 g/lOO cm3 solution of PVA.Data calculated taking a polymer adsorbed layer thickness of 40 nm. - -, assuming a PVA concentration of 0.2 g ~ m - ~ in the adsorbed layer; -0-, assuming a PVA concentration of 0.5 g ~ m - ~ in the adsorbed layer. The data presented in fig. 5 show a slow rise in applied pressure at the longer separation distances and then a steep increase as the distance of separation approaches 60 nm. At the latter distance, the curve becomes almost vertical and confirms the steep rise observed by the reflectance technique. These data also agree with those from reflectance measurements calculated on the assumption of ~ 0 . 5 5 g ~ m - ~ PVA in the film, and hence confirm the high polymer concentrations formed in the film.DISCUSSION Basic measurements of interaction forces demand either a molecularly smooth surface, eg., r n i ~ a , ~ , ~ or elastic materials whose surfaces deform to approach closely smooth surfaces under an applied p~essure.~*~ Earlier work had shown that poly(is0- butylene) rubbers could be used to produce an optically smooth spherical surface and that such a surface could be used in conjunction with an optically polished glass surface to study electrostatic interaction force^.^^^ The disadvantage of this method was that it involved the use of two different adsorbing surfaces. In order to avoid this problem in the nresent work. two silicone rubber lenses were used. It was also40 ADSORBED LAYER INTERACTION 1 I I I 1 I I 20 LO 60 60 100 120 140 h /nm FIG.5.-Pressure against distance of surface separation, h, obtained using multiple beam interfero- metry and a 0.2 g/lOO cm3 solution of PVA. --& in water; 0, in 0.1 mol dmW3 sodium chloride sodion. found that these were easier to mould, more reproducible in moulding and had a better optical transparency than the poly(-isobutylene) rubbers. The surfaces of the silicone rubbers are presumably mainly composed of siloxane and methyl groupings although the surface energy of 40 mN m-l estimated by Fuller and Tabor l4 suggests a fairly polar surface. The poly(-methylmethacrylate) surface coatings which were necessary to form the multiple lenses required for interferometry also had the advantage of producing a polar surface for the adsorption of PVA.The macromolecular adsorbate chosen was PVA because a characterised sample was available and because it is frequently used as a disper~ant.~~ Despite the many limitations of this material in terms of heterodispersity, both with regard to degree of substitution and molecular weight, the fact that it is essentially a block copolymer ensures that it adsorbs on relatively inert surfaces. The material used, Alcotex 88/10, had a weight average molecular weight of 45 000 and according to Garvey et aZ.,13 after fractionation, the highest fraction had a weight average molecular weight of 67 000. It is clear, therefore, that this material could contain even higher molecular weight material, lo5 or greater, and that under the low surface area and relatively long equilibration times used in the present experiments there is a high probability that the highest molecular weight material would be preferentially adsorbed.Initially, following on previous work5 a reflectance method was used to estimate the form of the applied pressure against distance curves. This established that the concentration of PVA in the thin liquid film formed between the rubber surfaces had a concentration of m0.55 g cm-3 or higher. At this high concentration it was not possible to establish uniquely the distance between the rubber surfaces owing to the rapid change in refractive index with distance from that of the initial solution. How- ever, the high gradient of the (pressure, distance) curve which was independent of the absolute determination of distance, indicated that the compressibility modulus of the thin film was very high, becoming comparable with the elastic modulus of the rubber.F .W . CAIN, R . H . OTTEWILL AND J . B . SMITHAM 41 This observation, together with the high PVA concentration, indicated the possible formation of an elastic gel between the surfaces. However, the long-term stability of the film under pressure and the reversibility on removing the pressure, indicated that the polymer molecules remained firmly adsorbed on the surfaces. The development of the multiple beam interferometric apparatus established that the rapidly rising pressure (>2 x lo4 N m-2) occurred at a distance of ~ 6 0 nm. In the high pressure region the gradient of the interferometric data was identical with that of the reflectance data, thus establishing the mutual compatibility of the two sets of data.With the interferometric technique the results were also extended to longer dis- tances of surface separation and lower pressures. At the lowest pressure measured, 5.5 x lo3 N m-2, the distance between the poly(-methylmethacrylate) surfaces was m 120 nm and extrapolation to the zero pressure axis, to obtain the distance of initial interaction, ho, gave a value of 160 & 20 nm. This would suggest, if interaction begins at the periphery of the adsorbed layers, a distance of about 80 nm for the thickness of the adsorbed layers. This appears to be of the same order of magnitude but a little longer than some of the values quoted for thicknesses obtained by different method^.^^*^^*^^ Inevitably, in these cases, the thickness is defined by the method of measurement ; it is clear, however, that the thicknesses are not necessarily physically equivalent.In fact, using a PVA sample with a molecular weight of 86000, van Vliet 25 found an h, value of 100 nm from measurements on aqueous foam films. This would suggest 50 nm as the extension of the adsorbed layer (h0/2), a value consideraby larger than the figure of 20 nm found by ellip~ometry~~ for the optical thickness of an adsorbed layer of PVA (number average molecular weight = 30 000) at the air-water interface. Garvey et aZ.,13 using PVA adsorbed on polystyrene latices, obtained a value from hydrodynamic measurements for the adsorbed layer thickness of 38.2 & 3.0 nm with a PVA fraction having a weight-average molecular weight of 67000.The latter authors also obtained data on the variation of adsorbed layer thickness with molecular weight, which give for a molecular weight of 87 000 & 6000 an adsorbed layer thickness of 80 10 nm. If it is remembered that the present technique would allow the high molecular weight fraction to adsorb preferentially at the interface and that, as suggested by van Vliet,2s some of the polymer tails could extend a substantial distance into the solution, then the value of h0/2 obtained in the present work is not unreasonable. The compressibility of the thin film as expressed by, Y = -(aP/a In h)h where P = applied pressure, was found to have a value of 1.2 x lo4 N m-2 at h = 100 nm.This, if interpreted as an elasticity modulus, would suggest the formation of a weak visco-elastic gel. However, whether this is due to the overlap of adsorbed layers, either monolayer or polylayer, to the entrapment of molecules in the layer during drainage or the variation in the physical properties of PVA solutions with volume fraction, is not at present clear. Under the conditions of the present experiments, the van der Waals attractive forces are essentially negligible between two rubber surfaces separated by about 100 nm in a liquid of similar refractive index. Moreover, the experiments carried out in 0.1 mol dmW3 sodium chloride solution gave the same results as those in water hence indicating the absence of electrostatic forces arising from the overlap of electrical double layers.We therefore consider that fig. 5 represents the form of the inter- action curve for two surfaces in the presence of a macromolecular solution where it is known that the inacromolecule adsorbs strongly to the surface,42 ADSORBED LAYER INTERACTION The present indications are that for PVA the interaction behaviour depends very markedly on the rheological properties of the thin films, i.e., the variation in the visco- elastic properties with composition. It would seem that to investigate the region of steric stabilization covered by most current theories the investigation must be extra- polated to lower pressures and to longer distances. We will defer, therefore, a comparison with theory until such experiments have been successfully accomplished.Our thanks are due to the S.R.C. for the award of a CASE studentship to F. W. C. and a post-doctoral research assistantship to J. B. S. J. B. S. also acknowledges with thanks the award of an Eleanor Sophia Wood travelling fellowship from the Uni- versity of Sydney. The CASE studentship was held in conjunction with B.P. Limited, Sunbury, and we are grateful to Dr. R. J. R. Cairns for many helpful discussions. H. Freundlich, Colloid and Capillary Chemistry (Methuen, London, 1926). W. Heller and T. L. Pugh, J. Chem. Phys., f954,22, 1778. D. H. Napper, Ind. Eng. Chem. (Product Res. Des.), 1970, 9,467. A. D. Roberts and D. Tabor, Proc. Roy. SOC. A, 1971,325, 323. D. B. Hough and R. H. Ottewill, Colloid and Interface Science, ed. M. Kerker, Hydrosols and Rheology (Academic Press, N.Y., 1976), vol. IVY p. 45. J. N. Israelachvili and G. E. Adams, Nature, 1976,262,774; J.C.S. Faraday I, 1978,74, 975. J. N. Israelachvili and D. Tabor, Prog. Surface Membrane Sci., 1973, 7, 1. A. Doroszkowski and R. Lambourne, J. Polymer Sci., 1971, C34,253. A. Doroszkowski and R. Lambourne, J . Colloid Interface Sci., 1973, 43, 97. lo L. Barclay and R. H. Ottewill, Spec. Disc. Faraday Soc., 1970,1, 169. R. J. R. Cairns, R. H. Ottewill, D. W. J. Osmond and I. Wagstaff, J. Colloid Interface Sci., 1976, 54, 45. l2 A. Homola and A. A. Robertson, J. Colloid Interface Sci., 1976, 54, 286. l3 M. J. Gamey, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1976, 55, 440. l4 K. N. G. Fuller and D. Tabor, Proc. Roy. Soc. A, 1975,345, 327. l6 D. Caballero, J. Opt. SOC. Amer., 1947, 37, 176. l7 S. Tolansky, Multiple Beam Interferometry of Surfaces and Films (Oxford University Press, l8 J. N. Israelachvili, J. Colloid Interface Sci., 1973, 44, 259. l9 P. A. Lewis, Ph.D. Thesis (University of Bristol, 1973). 2o H. Hertz, Miscellaneous Papers (Macmillan, London, 1966). 21 Polymer Handbook, ed. J. Bandrup and E. H. Immergut (Interscience, New York, 1966). 22 F. W. Cain, Ph.D. Thesis (University of Bristol, 1978). 23 Th. F. Tadros, Particle Growth in Suspensions, ed. A. L. Smith (Academic Press, London, 1973), p. 221. 24 E. L. Zichy, J. G. Morley and F. Rodriguez, Chemie, physikalische Chemie irnd Anwendungs- technik der grendachenaktiven Stofe (Carl Hanser Verlag, 1973), p. 241. 25 T. van Vliet, Mededelingen Landboidwhogeschool, Wageningen, 1977,77, 1. P. H. Carnell, J. Appl. Polymer Sci., 1965, 9, 1863. London, 1949).

ISSN:0301-7249    

DOI:10.1039/DC9786500033

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

GENERAL DISC USSIO N Dr. W. van Megen and Dr. I. Snook (Melbourne) said: In connection with hydra- tion forces a few comments may be relevant: (1) Recent Monte Carlo (IvfC) calculations, of the structure of dense Lennard- Jones liquids adjacent to solid surfaces, reveal a pronounced stratification of the liquid’s density profile (fig. 1). This stratification extends over 4 to 6 molecular dia- 0 2 6 Z/G a 10 FIG. 1 .-Density profile for a Lennard-Jones fluid of reduced bulk density of 0.84 between two solid surfaces. The solid at the right is represented by a hard wall ; the solid at the left wall is represented by a 10-4 potential - and a 9-3 potential - - - - - - . See Steele’s book for details of these potentials. meters, depending on the precise form of the pair potential and the liquid’s bulk den- sity.It should not be unreasonable to assume that the range of the consequential force is of a similar magnitude to the range of the liquid’s stratification. Extrapolating our calculations on simple liquids to water, this would imply a hydration force of range around 2 nm. (2) Steele’ shows that the potential energy of a fluid molecule in the vicinity of a solid surface is sensitive to the structure of the solid and which crystal plane of the solid is exposed. Our MC calculations show that the liquid’s density profile is par- ticularly sensitive to the precise form of the fluid-solid potential. This seems to be in accord with your findings. Since in your experiments there is an interplay between four different kinds of forces which may even be coupled, we wonder whether it would be possible to repeat these experiments with apolar solvents ultimately to pinpoint these hydration or sol- vent structure forces more precisely? To take up Levine’s informal comment on the absence of a crystallized liquid layer in the vicinity of the solid-liquid interface we remark that radial distribution functions in thin rectangular panels parallel to and at various distances from the solid surface indicate that the liquid near the solid surface is not crystal like, but has a structure very similar to that of the corresponding bulk liquid.Fig. 2 shows these panel distri- bution functions (dots) at various distances from the solid surface compared with the radial distribution function for the corresponding liquid.W. A. Steele, The Interaction of Gases with Solid Surfaces (Pergamon Press, Oxford, 1974), chap. 2.44 GENERAL DISCUSSION 3 , FIG. 2.-Panel radial distribution functions for a Lennard-Jones fluid (bulk density of 0.84) at various distances from the solid surface, indicated by heavy dots, compared with the bulk radial distribution functions. (a) z = 0 . 9 8 ~ ~ (6) z = 2.810, (c) z = 5 . 6 8 ~ . Prof. J. Th. G. Overbeek (Utrecht) said: Could the repulsion that you have called " hydration forces " be due to silica chains or silica gel particles possibly formed by hydrolysis of the mica and strongly adhering to the mica surfaces? Prof. A. Silberberg (Rehovot) said: What is known about the mica surface in con- tact with water? Could the structure be different to what is supposed? Could, for example, some of the components of mica have become polymerized and cross-linked leading to a surface layer swollen by water and actually representing a gel.Under such circumstances repulsion at 1-7 nm separation would not be too hard to under- stand. Dr. S. Levine (Manchester) said : Any firm conclusion from experiment on a force between charged mica surfaces other than the usual van der Waals and electric double layer forces depends on an adequate theory of the electric double layer. At concen- trations < of 1-1 electrolyte, the Poisson-Boltzmann (PB) equation, the basis of classical theory of double layer forces, is probably reasonable in aqueous systems, but in the range L10-2 mol dm-3, particularly at higher surface potentials, this equation becomes increasingly unreliable as the electrolyte concentration is increased.In the case of 2-2 electrolytes, the inadequacy of the PB equation occurs at smaller concen- trations and this failure is even more pronounced with unsymmetrical electrolytes. One of the corrections to the PB equation is due to the variation of dielectric constant with distance from the plate walls and the conjecture about hydration in this paper implies that the dielectric constant in the diffuse layer is reduced significantly over a distance of about 6 nm, whereas I would suggest a figure of 1 nm as more reasonable. It must beGENERAL DISCUSSION 45 stressed that there are a number of modifications to the PB equation, of which variation in dielectric constant is only one and not necessarily the most important correction (e.g.self-atmosphere-image and ion-size effects), and because of possible partial com- pensation, it is necessary to consider all the corrections simultaneously. Dr. J. W. White (Grenoble said: I should be glad if you would say more about the experimental characteristics of the hydration forces mentioned in your paper in rela- tion to structural models for water at alumino-silicate interfaces. The essential thrust of the diffusion coefficient measurements made by Olejnik and White [ref. (19) of your paper] was that the water is remarkably unstructured, at least from the point of view of dynamical measurements. Dr. E. J. W. Verwey (Utrecht) said: In the 1930's colloid chemistry developed from a collection of" schools " into an integrated science.The work of Frumkin, connect- ing colloid chemistry and electrochemistry, the experiments of Derjaguin on " thin layers ", and the early calculations of Levine on the interaction of double layers were among the first indications of this integration process. It was officially recognized by the Faraday Society when it organized a General Discussion on the Electrical Double Layer, which was intended to be held in September 1939 in Cambridge but could not take place owing to the outbreak of the war. Although I have not been active in colloid chemistry in the last 33 years (we wrote our book in the winter of 1944-1945) I have always been interested in its interactions with other fields. After the war colloid chemistry has been generally accepted as part of physical chemistry but it is also clear that our understanding of lyophilic colloids is becoming of increasing importance for biochemistry.Israelachvili's paper and especially his observation of " hydration repulsion " (and similar indications in other papers at this Discussion) induces me to suggest a new aspect of this link with biochemistry. I am referring to " hydrophobic inter- action ", which plays an important part in for instance the attraction between the hydrophobic sidechains in the folding process of proteins. The nature of these forces is not quite clear, although we know that the gain in free energy is mostly of an entropic nature. This must be interpreted as an increased amount of order of the water molecules in the neighbourhood of the hydrophobic substance.The " hydration repulsion " between two mica plates at very short distance is obviously connected with a similar phenomenon : an increased " crystallisation " close to the mica surface. In this special case the effect may be reinforced by a paralel- lism in the structure of mica and ice. The more general nature of the phenomenon of the increased amount of order close to a " hydrophobic " wall suggests, however, that there must be another reason for this effect, especially if one considers that at thefree surface of water the situation is the other way round. Here there is more disorder in comparison to the bulk phase (surface entropy is positive). A possible explanation is that the van der Waals-London forces between the hydro- phobic " wall " and the water molecules have the general effect of increasing the order of the latter, but a more detailed investigation of the thin layer in contact with different materials using the methods indicated in Israelachvili's paper may give more informa- tion and create a new link with biochemistry.Dr. J. N. Israelachvili (Canberra) said: Many of the queries raised concerning our experimental results and their interpretation are discussed in some detail in a paper by G. Adams and myse1f.l J. N. Israelachvili and G. E. Adams, J.C.S. Faraday I, 1978,74, 975.46 GENERAL DISCUSSION The possibility that the repulsive “ hydration ” forces are due to the steric repul- sion of solvated polymeric silica chains (or some other polymeric chains) protruding from the mica surfaces cannot be excluded.However, I consider this unlikely for the following reasons : First, the aqueous region between the mica surfaces has the same refractive index as the bulk even when strong “ hydration ” forces are present, and even after the mica surfaces have been in water for more than one day.l Further, the attractive van der Waals forces do not appear to be in any way affected or modified by the presence of these forces. These findings allow us to conclude that the water adjacent to mica sur- faces is not the highly contaminated “ anomalous ” water of bygone days, and that the surface concentration of silica polymers, if they exist, must be very low, and yet sufficient sometimes to produce fairly strong repulsive f0rces.l Second, the hysteresis effects, discussed below, are difficult to interpret in terms of a dilute surface concentration of polymeric chains, unless these are somehow able to control the position of the OHP.Third, the “ hydration” forces are only weakly dependent on ionic strength and pH-an observation that also appears difficult to reconcile with solvated polymer- stabilized interactions. Fourth, a number of experimental studies on the self-diffusion of water, the viscous properties of water, and the heats of immersion of water2 at silicate and other clay mineral surfaces as well as at the ice-water interface have indicated behaviour different from bulk water decaying exponentially away from the surfaces with decay lengths close to 1.0 mn. Since the exponentially decaying “ hydration ” forces were also found to have a decay length of -1.0 nm it is reasonable to conclude that the same phenomenon was being observed in all these different studies.This being so, poly- meric silica chains would have to be invoked to account for some of these observations as well. Also related to this matter is the widely different swelling properties of clays such as the montmorillonites, where the amount of swelling in water has been found to be correlated with the crystallographic b-dimensions of the surface lattices, which closely match that of ice.3 In answer to Levine’s query, we analysed more than 50 (force, distance) curves before concluding that the “ hydration ” forces represented an additional force and not a modification of the double-layer forces.Of course, any theoretical insight as to how the effects Levine mentioned affect the double-layer forces will be welcome. Silberberg asked what is known of the mica-water interface. The mica surface at the cleavage plane is chemically inert in aqueous electrolyte solutions in the normal pH range of the experiments (pH 6-7), and we have verified that our micas do not hydrolyse and that, as expected for micas, they do not swell over the time period of the experiments, about 1 day [see also ref. (l), appendix 11. In answer to Hills’ informal remarks, I think it is important to remember that not only is the mica surface a solid surface, in contrast to the free water surface and the mercury surface, but that the mica surface is also an oxide surface to which water molecules can hydrogen bond.There is also the additional crystallographic simi- larity between the mica and ice lattice which could favour epitaxy [see also ref. (l), section 41. Details will be found in ref. (1). J. N. Israelachivli and G , E. Adams, J.C.S. Furuday I, 1978,74, 975. E. Nyilas, T. H. Chiu, D. M. Lederman and F. J. Micale, Colloid and Interface Science (Aca- demic Press, 1976)) vol. V. 111, p. 471. I. Ravina and P. F. Low, Clays and Clay Minerals, 1972,20, 109.GENERAL DISCUSSION 47 Verwey’s suggestion that “ hydration ” forces may be related to hydrophobic interactions, and of their importance in biological systems is, indeed, the subject of some current theoretical interest.l Finally, I should like to mention that any question like “ How far does the hydra- tion force extend?” is not easy to answer.These forces decay exponentially with distance, and do not stop abruptly at some separation. All that can be said is that in our experiments their effect was negligible (compared to the double-layer and van der Waals forces) at separations above 7.5 nm. Clearly, more work has to be done, e.g., with different solvents, at different temperatures, etc., before we can say more about the origin and nature of these forces. Prof. J. Lyklema (Wageningen) said: The issue whether or not hydration of sur- faces contributes to a repulsive force between colloid particles or between macrocopic bodies is still drawing much attention. The main difficulty is that usually several forces are simultaneously operative.Hydration forces tend to be invoked as contributing to the interaction if the sum of all other forces is inadequate to explain experimental observations. In doing so, imperfections in the theoretical picture of the “non- hydration ” forces are also interpreted as ‘‘ hydration ” forces. Israelachvili has done very elegant measurements, and he concludes that not all his results are explainable in terms of van der Waals attraction and double layer repulsion. As these experiments belong to the best that is available, it is a pity that the author has dubbed the unexplained extra force “ hydration force ” without investigating whether it is really due to hydration and not to some other phenomenon. The only fact that seems to be established is that this force is related to the surface properties of the mica.In fact, several properties of this additional force could be well “ explained ” by assuming that there are polysilicates extending from the mica surface into the solu- tion: (i) the number and extension of such polymers would depend on the process of cleaving and hence be different for different mica sheets (ii) the decay length of any steric repulsion, induced by such polymers could well be of the same order as that observed experimentally and (iii) the hysteresis phenomenon can be attributed to an irreversible reconformation of these chains. The main point I wish to make is the recommendation that the term “ hydration force ” be restricted to those forces where it is unambiguously established that hydra- tion is the sole responsible factor.Dr. J. N. Psraelachvili (Canberra) said: I agree with Lyklema that the use of the For the time being it would be term “ hydration ” forces was possibly premature. better to refer to them as “ additional ” forces. Prof. R. H. Ottewill (Bristol) said: Would you please outline the mechanism by which a mica surface acquires a charge and hence a surface potential. Were the surface potential values quoted in the paper obtained via the force measurements, or by an independent method? If the former, have you compared the results with those obtained by an electrokinetic experiment ? Would you also please comment on the nature of the hysteresis effects which you observed with the mica plates and provide details of the time scale of the experiment.Was this on a very short time scale, i.e., of the order of relaxation time for ions in the double layer, say s or less, or on a long time scale, say hours? I feel certain that the origin of the hysteresis observed in your experiments is quite D. Chan, D. J. Mitchell, B. W. Ninham and B. Pailthorpe, in Water, a Comprehensive Treatise, ed. F. Franks (Plenum Press, London, 1978), vol. 6, in press.48 GENERAL DISCUSSION different from that which we observed with montmori1lonite.l The explanation which we gave for this effect in terms of the rearrangement of a random array of plates to an ordered arrangement has been confirmed recently by neutron scattering experiments. Moreover, the fact that we observed the maximum effect in the most dilute electro- lyte systems would also appear to be in agreement with our interpretation.Dr. J. N. Israelachvili (Canberra) said: The effective surface potentials of the double-layer forces were obtained from the measured forces. No independent mea- surements of the potentials have yet been made, but this is being planned. I do not know by which " mechanism " the surface potentials or charge densities are estab- lished. In section 3 of my paper with Adams,2 a table is given of the chemical com- position of some of the micas used as determined by electron microprobe analysis, and the surface potentials as determined from the forces. It is noteworthy that those micas which exhibited low surface potentials had less Na and more K, though the amounts of Al, Fe and Mg also differed significantly.Hysteresis effects (or irreversible effects) were usually very small or non-existent, but on occasions large enough to be studied in some detail [see ref. (2), fig. 91. The distmce D/nm FIG. 1.-Schematic illustration of the variation of forces P with distance D showing the effects of hysteresis for two curved mica surfaces of radius R . The corresponding pressure P for two planar surfaces, given by the Derjaguin approximation P = a(F/bR)laD, is shown in the inset. - - -, maximum theoretical double layer force; -@-, first approach; -0-, subsequent approaches. general features are illustrated in fig. 1, in which the double-layer forces measured on the first approach in a given aqueous solution, e.g., measured -1 h after raising the concentration from to mol dm-3, were larger than those measured subse- quently, say -1 h to -15 h later (the measurements themselves take about 1 min per datum point). The exponential decay lengths of the repulsive forces were invari- ably the same on the first and subsequent approaches, and close to the theoretical Debye lengths of the electrolyte solutions.However, the magnitude of the forces on the first approach was greater than allowed for by double-layer theory (even assuming an infinite surface potential or charge density). For this reason I concluded that the hysteresis arises from an irreversible inward shift of the OHPs, in addition to any I. C . Callaghan and R. H. Ottewill, Furuday Disc. Chem. Soc., 1974,§7, 110. J. N. Israelachvili and G. E. Adams, J.C.S. Faruday I, 1978,74,975.GENERAL DISCUSSION 49 possible reduction of the potential or charge, during the first (forced) approach of the surfaces.By applying the Derjaguin approximation to the results for the force F against distance D for the curved mica surfaces one may obtain the corresponding pressure P against distance D for two planar surfaces (see inset, fig. 1). The " transition" region, wherein the OHP are presumably being displaced, shows up as a " plateau " region for the planar configuration at pressures usually close to P z 0.1 atm. This suggests the possible existence of a two-dimensional phase transition mechanism. The forces themselves, however, are still reversible in this " transition " region; the surfaces have to be brought much closer (closer than 5 nrn) before the forces become irreversible (hysteretic).Finally, hysteresis effects were generally accompanied by large " hydration " or '' additional " forces at smaller separations. Dr. J. W. White (Grenoble) said: My second question concerns the forces between alumino-silicate surfaces at low separations. Our original work using neutron diffrac- tion, and more recent work at very high energy resolution with instruments at the Institut Laue-Langevin in Grenoble, show that the diffusion of water in the crystalline swelling region of clays is probably different in kind from that in the osmotic region of swelling. This implies a quite different structure for the water in this region. Dr. J. Visser ( Vlaardingen) said : (1) How general are your observations; in other words, how far can your results be applied to other systems, such as polystyrene latices? (2) You do not mention the temperature at which you did your experiments. I suppose they were done at room temperature.What kind of effect may one expect at other temperatures, let's say at 40 "C and at 50 "C, particularly as regards the hydra- tion effects observed? (3) In all your measurements, you stayed away from the i.e.p.; would you please tell us why? Would you not get more information by measuring at that point in the sense that you reduce electrostatic contributions to the interactions ? (4) Suppose you achieved contact; is all the water then squeezed out from be- tween the adherents or not? (5) To what extent does surface deformation either account for your resuIts, or interfere with the interpretations ? Dr.J. N. Israelachvili (Canberra) said: We have yet to do more work on the ad- hesion forces and on the interactions at separations below 1.5 nm. What has so far emerged is that the forces that ultimately determine the adhesion are already evident at separations of -1 nm. Thus when the adhesion forces are strong the surfaces come into contact (in a primary minimum) at a separation of 0.0 & 0.4 nm relative to contact in uncleaved mica. This would allow for no more than a monolayer of water between the surfaces when in strong adhesive contact. In cases where the adhesive forces were weaker we noted that contact occurred a few Bngstroms further out. I am not sure what the i.e.p. of mica at the cleavage surface is, probably close to pH E 3. At pH NN 3 the adhesive forces are always much stronger (by 2 orders of magnitude or more) than at pH M 6-7, and the surfaces tend to tear up on separating them from contact.For this reason we stayed away from the i.e.p. All the experiments were carried out in a temperature controlled room at 20-22 "C. I do not know what effect changing the temperature would have. We shall try it. Surface deformation (flattening) occurs when the curved mica surfaces are brought50 GENERAL DISCUSSION close together against very strong repulsive forces. Such deformations were negligible at separations above 1.5 nm (see my paper with Adams for more details). As regards the applicability of our results to other systems, I would say that since the measured double layer and van der Waals forces are in good agreement with theory we may expect these results to apply more generally to other systems.At small separations, however, the forces often deviated drastically from theoretical ex- pectations and here the results, and the conclusions drawn from them, may not be generally applicable to other systems. Dr. B. Vincent (Bristol) said: I am wondering if the apparently very large values Lyklema reports for the " equilibrium " separation in the thin films stabilised by PVA might be due to multilayer adsorption at the aqueous/air interface. We have evidence' for such multilayers in the case of PVA adsorbed at the aqueouslpolystyrene interface, at the equilibrium PVA concentrations you have used (400 and 1400 p.p.m.), from both adsorption isotherms and adsorbed layer thickness (hydrodynamic tech- nique) measurements.Maybe such multilayer adsorption would not be so apparent from ellipsometric measurements since this technique relies on a significant refractive index increment between the adsorbed layer and the bulk solution. Although the first layer may have a reasonable refractive index increment, it could be that in the second (and subsequent) layers the coils are hardly distorted from their solution con- formations, and that therefore the refractive index increment relative to the bulk solu- tion is much less here. I would also query the shape of the molecular weight distribution assumed for the sample of PVA used by the authors. They have assumed a distribution which " tails " towards high molecular weights.We have carried out a g.p.c. analysis2 of a similar sample of PVA (admittedly not from the same suppliers, but also 88% hydrolysed poly(viny1 acetate) and of similar average molecular weight, 45 000). The distribu- tion tails in fact to low molecular weights, with a sharp cut off at high molecular weights (-67 000). Dr. Th. F. Tadros (Jealott's Hill) said: The " equilibrium " film thickness of PVA obtained by the authors for a sample of HviSc = 42 500 extrapolated to Ph = 0 is of the order of 70-80 nm. Such a value is a little higher than twice the hydrodynamic layer thickness (6) of a PVA sample of similar m.w. (Rw = 45 000) and similar acetate content, on polystyrene latex particles (330 nm diameter); 6 = 32.7 -i- 3.0 nm.3 Moreover, we have also shown that the adsorbed layer thickness increases as the particle radius increases and it depends on the surface properties of the latex partic1es.l Thus, these thick PVA films are to be expected and I do not feel there is a need to in- voke the presence of tails to explain the results, particularly if one realises that multi- layer absorption of PVA is a possibility.2 Most likely, at the plateau of the adsorption isotherm, the polymer coil rearranges and becomes more elongated normal to the interface (the volume occupied per molecule remains the same as in bulk solution, but the thickness of the adsorbed layer is greater than the diameter of the hydrodynamic sphere in solution).Prof. J. Lyklema and Dr. T. van Vliet ( Wageningen) said : For a number of reasons we rejected the idea of multilayer formation. In the first place it must be noted that Th.van den Boomgaard, T. A. King, Th. F. Tadros, H. Tang and B. Vincent, J. Colloid Inter- face Sci., 1978, 66, 68. M. J. Garvey, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1974,49, 57. M. J. Garvey, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1976,55, 440.GENERAL DISCUSSION 51 hydrodynamic thicknesses, measured at the PS/solution interface are at best circum- stantial evidence that in other systems multilayer adsorption can occur. More perti- nent are adsorption studies at GL boundaries, from which no indication for multi- layer formation could be 0btained.l More direct evidence stems from a number of experiments in which, after attain- ment of equilibrium, the pressure was reduced.Within the, admittedly not minor, range of error the same thickness was then found as when this film was made directly at the final pressure. The time scale to attain this new equilibrium state was of the order of an hour, which does not seem enough for polymer molecules to diffuse from the bulk through the film to the surface to establish a multilayer. Hence, we conclude that only convective liquid flow takes place. A third, more indirect indication is that a tenfold increase in concentration gives rise to not more than 15% increase of h at given Fs (our fig. 2). If multilayer adsorp- tion occurred, a much stronger dependence would be expected. Regarding the MW distribution, GPC analysis of PVA samples very similar or identical to ours and from the same supplier showed the distribution to approach the “ most probable ” one2 and no indication for a sharp shut-off, as found by Garvey et al.was obtained. Apparently this cut-off is typical for the specific sample used. Prof. A. Silberberg (Rehouot) said: It is my impression that the curves of fig. 1 in the paper are essentially osmotic dilution curves of the polymer solution trapped between the adsorbed layers of the film. Referring to the experiments, it is clear that due to the surface curvature at points a ” the pressure pa will be less than pat,,, and (pa - patmos) will approximately equal the applied suction. Suction not only causes partial draining of the fluid layer but also a reduction in the polymer concentration in the core region of the film.Polymer con- centration will drop until the osmotic pressure difference between the core of the film and the bulk polymer solution (which is in tube T) balances (patmos - pa). Convec- tion through the film will continue until the bubble b has disappeared. During this time there is a pressure difference pb - pa applied where p b > patmos > pa. The final stages of equilibration probably involve diffusion of polymer from within the core layer of the film to the bulk supply. The (overall) thickness corresponding to two adsorbed layers with an effectively zero thickness core layer, i.e., zero polymer con- centration between the adsorbed layers corresponds to p b = pa - patmos = n, where 7r is that part of the osmotic pressure of the solution which is due to the polymer solute.On the other hand, when Ph = 0 ( p a = patmos), the film thickness will tend to corre- spond to that of two adsorbed layers plus that of a core layer, at least one undistorted polymer coil diameter thick. We see that for PVA 205 (400 p.p.m.) for example h N 80 nm whenp, = 0 and h N 40 nm whenp, = 50 N m-2. The film thickness 80 nm atp, = 0 agrees reasonably with two layers of 20 nm each and a coil diameter of 40 nm, whereas h = 40 nm at Ph 21 50 N m-2 corresponds to two touching adsorbed films. A pressureph 51: 50 N mV2 is a reasonable osmotic pressure for a 400 p.p.m. PVA 205 polymer solution. The data for the other polymers show similar behaviour. The agreement is approximate but is close enough to what may be expected from experimental accuracy.I do not believe that the explanation offered by the authors can be right. The exponential distribution (whether of tails or of other segments) has been calculated against an (essentially) zero concentration bulk solution. A different case arises 6 6 J. M. G. Lankveld and J. Lyklema, J. Colloid Interface Sci., 1972, 41,466. B. J. R. Scholtens, Meded. Landbouwhogeschool, Wageningen, Neth., 1977, 77, 7.52 GENERAL DISCUSSION when we deal with systems at finite concentration. The adsorbed layers if brought close to each other would tend to equalize concentrations and the few long tails would collapse or penetrate the other side. In calculations of the stable separation distance between two polymer molecules, Flory and Krigbaum considered the free energy minimum which is a compromise between strong overlap (a higher free energy of mixing and a lower free energy of distortion) and small overlap (a lower free energy of mixing and a higher free energy of distortion).In the case of the approach of two colloid surfaces, irreversibly coated by polymers, similar problems arise, but different considerations apply. As Hesselink, Vrij and Overbeek have shown when the polymer bulk concentra- tion is zero it is the osmotic (mixing term) repulsion which dominates. At finite concentration, the situation is more complex. If the polymer film is in equilibrium with polymer in solution the case discussed in my paper at this Discussion is approached, If adsorption is irreversible, there will be a tendency for coated colloid particles and polymer in solution to mix as though we had two molecular weight species of the same polymer in solution.In this case, in addition, the coated colloid particle is structurally different from the polymer, and long range van der Waals forces arise and may influence interaction between the colloid particles. Lyklema and van Vliet indeed assume that polymer is irreversibly adsorbed, but that in other respects their films reach equilibrium. More than a possibility exists, however, that in the draining of the film more polymer molecules than required for equilibrium were trapped and that their presence enhances the film thickness even more. " Trapping " would be most effective since the diffusion coefficient of such polymer molecules must be expected to be extremely low.h t "T" pa I Prof. J. Lyklema and Dr. T. van Vliet ( Wageningen) said: Silberberg raises a num- ber of points regarding the interpretation of equilibrium film thicknesses in polymer stabilized films. The main problem appears to be whether or not there are polymer molecules in the film between the two adsorbed sheaths. A similar question has been asked by Tadros and by Vincent. The presence of such molecules would require considerable modification of the theory by Hesselink et al. In our (semi quantitative) examples of computations we neglected any polymer remaining within the film after establishment of the stationary state. The main arguments for this decision are: 1. The reversibility of Fs as a function of pressure, i.e., as a function of h: a given Fs(h) situation can be obtained both from the side of higher Fs reducing the pressure or from the lower side by increasing it.The time to attain the new equilibrium thick- ness is of the order of an hour and apparently too fast to be attributable to the diffu- sion of polymer molecules. Our conclusion is that the rate of adjustment of the newGENERAL DISCUSSION 53 situation is determined by convective flow, so that, apart from the adsorbed polymer, the interior of the film must have roughly the same composition as the bulk. 2. Accepting that there is some polymer between adsorbed layers, we inferred from the fact that a tenfold concentration increase (from 400 to 4000 p.p.m.) increases h at fixed pressure by only z lo%, that the contribution of any molecules between the adsorbed layers is small and we decided to neglect it in this stage of the work. Some additional comments that can be made in this connection are: (i) the chemi- cal potential of the water is mainly determined by the glycerol (1 molar) hence there is no reason to invoke polymer concentration changes as the most likely way to counteract hydrostatic (or, for that matter, capillary) pressures and (ii) drainage of the film pro- ceeds by marginal regeneration and/or by the sucking into the border of thicker regions.In other words, it is, at least in part, of a convective rather than of a diffusive nature. This may be one of the major differences with the measurements by Cain et al. Dr. P. Walstra ( Wageningen) (communicated) : The system PVA 205 at 400 p.p.m.of Lyklema and the PVA 88/10 at 0.2 g/lOO cm3 of Cain appear to be quite similar. But in the comparable range of distances (h = 50-60 nm) the film pressures measured by both groups differ almost exactly by a factor 1000, Cain’s pressures being higher. How can this be explained? Prof. J. Lyklema and Dr. T. van Vliet (Wageningen) said: One of the factors that may be responsible for the different pressures at given range of interaction between measurements by Cain et al. and ours is the amount r of PVA adsorbed. In our case T - 3.1 mg m-2 while from the data by Cain et al. it can be inferred that at a bulk concentration of 0.5 g cm-3 Tis of the order of 20 mg m-2. This difference, in turn, can be due to the quite different mechanisms by which the films were formed in the two cases.As outlined in the discussion remark by Lyklema to Cain et al., the history of the film plays an important role. In particular, the different surface rigidities in the two cases deserve attention. For rigid films more experimental information is clearly needed to settle this point. Apparent stationary state thicknesses may be found that do not represent true equilibria. They are due to the very slow drainage of liquid from the film. Dr. J. B. Smitham (Bristol) said: No entirely satisfactory explanation can be offered at this time. We have examined our calibration procedure closely with special atten- tion being given to the measurement of the applied force, the area over which the force acts and the equating of the applied force to the force of steric repulsion.Direct application of forces comparable with those obtained by our earlier extra- polation procedure confirms that the forces are approximately equivalent and accurate to within a factor of two or three. The error is greatest at very low applied forces. At separations of order 100 nm, the force is x4 x N and this increases to 2.5 x For the PVA films the first detectable interactions occur at separations around 100 nm (fig. 5 of our paper). Only a slight change of shape of the FECO fringes is observed and it is not until the separation has become closer to 75 nm that the fringes show a marked flattening, corresponding to a flat thin film area. Thus in the region 75-100 nm the area over which the interaction occurs is less well defined.An additional criticism that has been made of the PMMA surfaces is that their surface roughness could increase the area over which the force is applied. However, electron micrographs of N at separations near 60 nm. The area over which the force is applied is subject to some uncertainty.54 GENERAL DISCUSSION shadowed carbon replicas of the surface did not reveal any gross defects of the surface. This was strongly confirmed by the nature of the FECO fringes which faithfully repro- duced any irregularities in the contact area. Moreoever, an approximate estimate of the roughness can be made by calculating the distance corresponding to half the width of a fringe. This is an overestimate because the fringe width is determined by the condition of the silver layer and not only by the smoothness of the transparent over- layers, whether they be mica or PMMA.Nevertheless, the maximum asperity height was 10 nm. Roughness of this order is not likely to cause the thousandfold dis- crepancy commented on by Walstra. The equating of applied pressure with the steric repulsion in a good solvent ap- pears straightforward. Our experiments indicate that the effect of added electrolyte For this reason electrostatic repulsion has been neglected since it was not significant. The repulsive pressures obtained in the compression experiment seem quite high. However, several theories exist for predicting the free energy change on the approach of two sterically stabilised flat plates. The steric pressure can be obtained by taking the derivative of the analytical expressions for the free energy change. Using appro- priate parameters for PVA and calculating theoretical curves of steric repulsive pres- sure against distance, we find that the calculated pressures are of the same order of magnitude as those observed experimentally.However, the theory predicts that the interaction should occur at smaller distances than those observed. Finally, it is interesting to note that Sonntagl found values of the repulsive pres- sures intermediate to those of Lyklema et al. and ourselves at comparable surface separations for PVA films. mol dmV3 NaC1) on the repulsive pressure is small. Prof. J. Lyklema (Wageningen) said: In trying to explain the differences between our free liquid film approach and the procedure adopted by Cain et al.I wonder to what extent the results may be influenced by the drainage pattern of the film, prior to the attainment of the stationary state. One typical feature of the free film method is that after formation a drop or dimple forms that after some time is sucked into the border. After this has happened the film is visually plane parallel, as can be confirmed within 5 nm by scanning. This step appears not possible in the drainage from between two rigid walls. Dr. J. B. Smitham and Prof. R. H. Ottewill (Bristol) said : In both types of apparatus we have used, continuous monitoring of the film area is possible. This can be achieved in the reflectance apparatus by direct viewing of the illuminated area and in the mul- tiple beam apparatus by direct examination of the FECO fringes.The latter provide an extremely sensitive method of monitoring the film profile. Thus any dimple formed by compression of the rubber is immediately visible and drainage of liquid and recovery of the dimpled surface to a plane interface can be monitored. Dimples only occur if the surfaces are pushed together rapidly. It has been our experience, however, that by using slow application of pressure, with precise fine control of the micrometer drive, the formation of dimples can be avoided. Dr. J. Klein (Rehouot) said: There are two related questions I would like to ask of (a) What is the resolution of the multiple beam interferometric technique as used (b) Can they give an estimate of the size of surface asperities both on the silvered Cain, Ottewill and Smitham.in their experiments ? H. Sonntag, Croatica Chem. Acta, 1976,48,439.GENERAL DISCUSSION 55 silicone rubber surface and on the poly(methylmethacry1ate) surface on which poly- mer is adsorbed? Dr. J. B. Smitham and Prof. R. H. Qttewill (Bristol) said: The resolution of the technique is limited by the measurable wavelength shifts of the fringes of equal chro- matic order (FECO). The question of the surface asperities was dealt with in some detail in the reply to Walstra. As pointed out there, the maximum size of the asperities can be related to the half-width of the fringes and this was estimated to be about 10 nm. In effect, this is also the resolution of the technique. The reproduci- bility of the method is well within these limits.The surface separations involved in the measurements are in the 60-120 nm and hence are large compared with the resolu- tion. The experimental accuracy is thus adequate to ensure meaningful measurements. Prof. A. Silberberg (Rehouot) said: In my comment on the work of Lyklema and van Vliet I have already pointed out the need to consider the fate of the bulk solution between two approaching surfaces. If equilibrium is to be discussed then clearly there must at all times be equilibrium between the film, the trapped unattached polymer and the bulk solution per se. Whether in equilibrium, or out of it, the presence of a polymer solution of finite concentration tends to give thicker films, certainly in cases where the adsorbed layers are (effectively) irreversibly attached.Direct comparison between data is, however, made very diAicult by the fact that different polymers, different solvents and different surfaces were used in these and in the measurements of others. The paper does not detail the time to equilibrium but I would judge that a wait period of the order of 25 min, though no apparent change in film thickness was noted, is too short. A more than small possibility exists therefore that present results do not reflect equilibrium values. The method is one of great beauty, however, and flexible enough to permit most of the questions raised to be answered properly in the future. Dr. J. B. Smitham and Prof. R. H. Qttewill (Bristol) said: Silberberg raises a num- ber of interesting points about the attainment of equilibrium in these studies.Quali- tatively, it takes several hours after the addition of polymer solution to the bare sur- faces before a stable film is formed when the rubbers are compressed. It was our ex- perience in a study by ellipsometry of the adsorption of gelatin into silver bromide surfaces that after about six hours both the surface excess concentration of gelatin and the optical film thickness reached a constant va1ue.l For this reason, compression studies were not commenced for a period of between 14 and 24 h after the addition of polymer solution. Thus we assumed that the surfaces were in adsorption “ equili- brium ” with the bulk polymer solution phase. We have not investigated in detail the effect of bulk polymer concentration on the equilibration time.The second equilibrium to consider is the “ approach equilibrium ” in the thin film which is formed on the close approach of the surfaces. The experimental evidence obtained, so far, indicates that this ‘‘ approach equilibrium ” was not a sensitive func- tion of electrolyte concentration, or bulk polymer concentration. Once the film had formed it remained stable for periods of several hours, i.e., although the film may not have been in true thermodynamic equiIibrium, it appeared to be so within the time scale of the experiment and it was not practicable to wait any longer before changing the applied pressure. We are in agreement with Lyklema and van Vliet that changing the bulk polymer concentration does not cause a marked change in repulsive pressure.T. J. Maternaghan and R. H. Ottewill, J. Phot. Sci., 1974, 22,279.56 GENERAL DISCUSSION This does not hold, however, if the polymer desorbs from the rubber surfaces; when this occurs the repulsion pressure decreases dramatically. Dr. Th. F. Tadros (Jealott’s Hill) said: The concentration of PVA in the thin liquid film between the rubber surfaces found by the authors, namely 0.55 g cm-3 seems to me extremely high. At such separation of -65 nm, this should correspond to an adsorption value of the order of 18 mg m-2 (if there is no polymer entrapped between the adsorbed layers), an extremely high value never obtained before on other surfaces, e.g. polystyrene, AgI, silica etc. The surface used by the authors is PMMA and ad- sorption of PVA on this could be different, but it is highly unlikely that such high adsorption value will be obtained.Dr. J. B. Smitham (Bristol) said: The reflectance method measures the refractive index of the thin film between the two silicone rubbers. Since the unadsorbed PVA is not removed, it is possible that, in addition to a PVA layer that is strongly adsorbed to the rubber surface, there are other layers weakly associated with the adsorbed layer. Indeed a study of the drainage curves as a function of increasing time of ad- sorption supports this view. Such multilayers would contribute to the refractive index of the thin film while not necessarily contributing to the surface coverage by the PVA. Thus what is determined by our experimental technique is the total polymer concentration between the surfaces.Adsorption isotherms obtained by centrifuging a dispersion stabilised by PVA may well remove the multilayers and measure only that PVA that is strongly adsorbed to the surfaces involved. Dr. A. Lips and Mr. E. J. Staples (Port Sunlight) said: In connection with studies of the adsorbed layer thickness of PVA on polystyrene latex particles,l we have performed osmotic pressure measurements on concentrated PVA solutions. We used the same polymer, Alcotex 88/10, as that employed by Cain et al. The results are summarised in fig. 1. At low polymer concentrations, C, the osmotic pressure, II, is consistent with the a value of the Flory Huggins parameter x 21 0.48. However, the observed behaviour indicates deviation from the Flory Huggins model in the direction of x increasing with C which is suggesting substantial attraction between the polymer molecules. This view is supported by the highly viscous, approaching gel-like nature of the solutions. Direct measurements of osmotic pressure for concentrations >0.2 g cmm3 have so far proved difficult. Nevertheless it can be inferred from the optical behaviour of more concentrated solutions that dII/dC is continuously and rapidly increasing with C, as suggested in fig. 1. The osmotic behaviour thus indicates the absence of a phase transition, and this has been confirmed for concentrations up to 0.45 g ~ m - ~ . Our measurements lend support to the view proposed by Cain et al. that the steric forces in their system are largely controlled by the compressibility of highly concen- trated polymer solutions. A quantitiative evaluation of this suggestion can be attempted if it is assumed that the approach of the two surfaces is accompanied by negligible change of adsorption and that the intervening polymer solution is sufficiently concentrated so that it can be treated as effectively homogeneous across the gap. The applied force, i.e., the steric force, can then be taken as equal to the differ- ence between the osmotic pressure of a polymer solution of concentration correspond- ing to that in the gap and the pressure of a solution representing conditions far away from the surface. The former osmotic pressure is usually dominant. Comparing our osmotic pressure measurements with the measurements of steric D. S. Duclcworth, A. Lips and E. J. Staples, this Discussion.GENERAL DISCUSSION 57 C/g ~ r n - ~ FIG. 1 .-Main diagram represents osmotic pressure measurements on PVA, Alcotex 88/10. The full lines are theoretical expectations based on Flory-Huggins theory for the values of x as indicated. Insert represents fig. 5 of paper by Cain et al. [applied pressure plotted against (separation)-'] force (fig. 5 of Cain et al), we can obtain a reasonable representation in terms of the homogeneous model of the dependence of the steric force on separation if the con- centration at a separation of 60 nm is taken as -0.2 g cm-3 (fig. 1). The quality of the fit may be fortuitous. Nevertheless, the value of osmotic measurements on concentrated solutions both in assessing a polymer system for con- formity to theoretical models and in providing a base-line for predicting steric forces is clearly demonstrated.

ISSN:0301-7249    

DOI:10.1039/DC9786500043

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Mechanical Spectroscopy of Colloidal Dispersions BY JAN MEWIS AND GUSTAAF SCHOUKENS Department of Chemical Engineering, Katholieke Universiteit Leuven, de Croylaan 2, B-3030 Heverlee, Belgium Received 19th December, 1977 The mechanical properties of colloidal dispersions are closely related to their stability parameters. Unfortunately, the rheological characteristics which are normally used, such as viscosity and static elasticity, measure the global behaviour. It is extremely difficult to extract from such characteristics detailed information about the structure. Therefore, there is a need for more adequate experimental techniques . The construction and the potential applications of a rheometer, in which an oscillatory movement is superimposed perpendicular to a steady shear flow, are discussed.Measurements on carbon black dispersions are carried out, and the relaxation spectra obtained for the sheared dispersions are compared with theoretical predictions based on a chain-like structural model. In this way, informa- tion concerning interaction forces and structural parameters is obtained. Mechanical measurements have been widely used to collect information on the structure of materials. The technique has been most successful on materials which show a time and frequency dependent response to stress and strain. The resulting viscoelastic behaviour can be represented by a characteristic time function, the relaxation spectrum H(z) which is used in mechanical spectroscopy. Clearly, a spectrum provides more information about structure than do viscosity or static elasticity.However, the available viscoelastic data on colloids have not contributed much to our understanding of structure. In part, experimental difficulties are responsible for the lack of success, the oscillations tend to affect the structure to be measured. In addition the spectra obtained do not have any prominent feature^.^-^ Recently, the viscoelastic behaviour of dilute, thixotropic dispersions under shear has been measured by means of relaxa- tion and oscillatory measurement^.^ The results seemed promising and consequently an experiment was set up to explore the mechanical behaviour of flowing colloids. In general, a given rate of shear entails a corresponding degree of structure in shear sensitive systems. If small oscillations are superimposed on the steady state shear, they do not further affect the structure. The oscillatory velocity can be chosen to be parallel or perpendicular to the steady state flow.In the former case the coupling between both modes of flow is stronger than in the latter. This effect shows up in the calculation of the spectra froin the oscillatory data.5 Therefore, the orthogonal superposition technique was selected. EXPERIMENTAL The general layout of the apparatus is given in fig. 1. The measuring cell (E) consists of two coaxial cylinders (Couette geometry). A variable speed motor (F + G) connected to the external cylinder generates the stationary shear flow. The inner cylinder is kept in position by two membrane springs (D). An electromagnetic vibrator on the same cylinderJ .MEWIS A N D G . SCHOUKENS 59 provides the oscillatory movement, which is detected by means of a linear displacement transducer (A). The geometry of the cell must ensure a nearly constant shear rate through- out the sample because the structure changes with shear rate. In Couette geometry the stresses depend on radius. Owing to the pseudoplastic nature of colloidal dispersions, a difference in stresses enhances the variations in the rates of shear. Hence the gap must be as narrow as possible. In the present instrument a radius ratio of 1.02 has been realized. This value limits the possible differences in shear rate to 10% if the power law index becomes as low as 0.2. With a gap size of 3 x lo4 m, one can expect particle size effects from aggregates and elementary particles (R = 6.5 x loF9 m) to be negligible, with qualifications for the fully developed network structures.As the instrument has only been applied to moderately concentrated, free flowing dispersions, the cylinders were not corrugated. The electromagnetic vibrator contains a permanent magnet (B) of 1 T with an annular gap. The inner cylinder carries an electric coil (C) at its top end, which fits in the gap of the magnet. An alternating current through the coil causes the required oscillation movement. A Solartron Transfer Function Analyser 11 70 is used as the variable frequency generator and for analysis of the complex (stress, strain) relation. In order to ensure a purely sinusoidal response, the oscillation amplitude can be reduced to 1 pm.The data provide the real (G') and imaginary (G") parts of a complex modulus which depends on shear rate (f) and frequency (a). Both parts of the modulus reduce to a single spectrum H(z,2j2), which is the most compact way of representing the data. At the same time any other viscoelastic parameter can be calculated from this spectrum. A shear rate dependent spectrum is used here. There are some fundamental arguments against this procedure7 but they do not interfere with the present analysis. It can be shown that the orthogonal superposition moduli are related to the spectrum by eqn(1): d(ln z). G"(7,P) = I-, H(2,2j2) - COT 03 1 + w2r2 Eqn (1) are identical in form with the normal relations from linear viscoelasticity. The spectra can, therefore, be calculated from the measured moduli in the same manner as in oscillatory experiments without superimposed flow.* RESULTS AND DISCUSSION The accuracy and the sensitivity of the instrument have been verified by means of measurements on homogeneous Newtonian and viscoelastic fluids. With a fluid of viscosity 19 Pa s, consistent results have been obtained down to the cHz frequency range.9 Viscosity and elasticity (first normal stress coefficient) have been computed from the oscillatory data with and without superimposed flow. They coincided with the corresponding values, measured directly on a Weissenberg rheogoniometer within the measuring accuracy of the latter in~trument.~ With the orthogonal superposition rheometer, measurements have been performed on structure-forming dispersions of carbon black (Neo Spectra Mark 11, Cities Services) in mineral oil4 at 20 "C.The samples are thixotropic. At rest they develop into weak, solid-like structures. Under shear the structures break down with time. To a large extent the shear induced changes are reversible. If the changes in structure are relatively slow, as during recovery after shearing, the spectra could be obtained as a function of time.4 In the present work, only equilibrium spectra are discussed. Fig. 2 presents the moduli measured on a 4.7% (volume) concentration at a shear rate of 13.1 s-l. In the terminal zone at low frequencies the G' curve tends to the theoretically required slope of 2, whereas G" attains a slope of unity. The60 MECHANICAL SPECTROSCOPY I FIG.1 .-Layout of the orthogonal superposition rheometer (A : linear displacement transducer; B: permanent magnet; C: electrical coil on inner cylinder; D: membrane springs: E: sample: F: gearbox; G: motor). f / H z FIG. 2.-Superposition moduli on a 4.7% carbon black in mineral oil dispersion (3 = 13.1 s-‘). 0, G”; f, G’.J . MEWIS AND G. SCHOUKENS 61 characteristic high frequency behaviour is also found in the relaxation spectra calcu- lated for the more dilute dispersions (fig. 3). All spectra extend from 1 x s to a variable upper limit which cannot be accurately determined for dilute dispersions. Curves 4 and 5 refer to recovered thixotropic structures. Once flow ceases the systems develop gradually into solid-like materials. The terminal zone then changes into a zone of constant G' (G' = 3.3 x lo2 N mP2 for curve 4, G' = 1.1 x lo4 N m-2 for curve 5).The spectra are wedge shaped and the slope becomes steeper with increas- ing shear rates. The data indicate a limiting high frequency slope of -1/2 for low shear rates at both concentrations. The present data differ from published work on 1 ool I I I I lo-* lo-' loo v FIG. 3.-Relaxation spectra of carbon black dispersions under shear. Curves 1-4: 2.2% carbon black (1, 9 = 26.2 s-'; 2, 9 = 13.1 s-l; 3, 3 = 2.62 s"; 4, after four days standing without shearing; curve 5,4.4% carbon black, after five days standing without shearing. other dispersions mainly through the presence of much more prominent spectral features. In order to analyse the data, we start from a simple chain model as used earlier in the description of static elasticity in colloids.lOvll The chains consist of elementary particles, held together by elastic springs.The spring force is caused by the inter- particle forces considered in stability theory. As such they provide a direct link between the rheology and stability of colloids. The particles in the chain affect the flow of the surrounding fluid and thus cause viscous dissipation of energy. Hence the chains are composed of dissipating spheres alternating with elastic springs. The behaviour of such structures under oscillatory flow can be calculated. As a matter of fact the model is identical to some of the earlier versions suggested for the simula- tion of polymer solutions.8*12 They all reduce to a ladder network of springs and dashpots (fig.4). All these chain models result in a discrete set of relaxation times z, given by: zp = zJp2 ('JI = 1, . . . N). (2)62 MECHANICAL SPECTROSCOPY FIG. 4.-Mechanical ladder network in the simulation of a chain of colloidal dispersions. The smallest relaxation time corresponds to the relaxation of subsections of a chain containing one spring. Larger values of zr, are related to the coordinated movement of increasingly larger sections of the chain. If an equivalent continuous spectrum is derived from eqn (2), or if the high frequency moduli are calculated, one finds the limiting behaviour : l3 ‘ G’ = G” cc m1/2 and H(z) K T ~ / ~ . (3) Hence, if simple chain elements are present, the system should give a spectrum with slope -1/2 at small times.Viscoelastic measurements can, therefore, be used to determine the postulated existence of chains. Fig. 3 provides some evidence that such a structure is present in the carbon black dispersions to hand. A slope of value 1/2 is only encountered if all the chains contribute in the same manner to the different relaxation mechanisms. Since one does not expect the various chains to be identical in size, only a fraction of the chains present can contribute to the longer relaxation times. This effect of polydispersity reduces the spectrum at larger values of z below the expected value, increasing the local slope. If the chain length is systematically decreased the theoretical slope of 1/2 might disappear. This behaviour could be responsible for the steeper slopes found at higher shear rates.Zimm14 has shown that hydrodynamic interaction between the particles leads to slopes of 2/3. This interaction does not require any superimposed stationary flow and, therefore, should also act without superposition. Fig. 3 shows that, in our dispersions, the steeper slopes disappear at zero rate of shear, making the Zimm explanation less likely. Clearly the presence of more complex floc shapes will also alter the spectrum. Except for the qualitative purpose of verifying the structure, the data can possibly be used in a more quantitative manner. The shortest relaxation time corresponds to the smallest relaxing subchain, i.e., a single bead-spring element. Such elements are always present except perhaps at very high shear rates.Fig. 3 gives 1.5 kHz as the highest relaxation frequency. Homogeneous fluids do not show any particular change at that frequency, hence the effect does not seem to be an instrumental artefact. The value of zmin is determined by the viscous dissipation caused by the particle movement and by the spring constant of the elastic interaction forces. Using Stokes’ law for the viscous force one can calculate the spring constant from the value of Zmin. We use the relation obtained for bead-spring models : l5 where yo = viscosity of the medium = 1.2 N s m-2 which leads to Hs = 3.7 x N m-’. The spring constant describes the (force, deformation) relation for particle doublets. Hence it measures the second derivative of the interaction potential at the equilibrium interparticle distance.For the materials under consideration it is difficult to obtain information about the interaction potential in another manner. Accord- ingly, the suggested method could be useful in stability studies of such systems.J. MEWIS AND G . SCHOUKENS 63 In principle the spectrum can also be used to estimate the chain size during flow. Normally, the shape of the terminal zone of the spectrum will depend on the chain size distribution, because not all chains can contribute to all relaxation times. Un- fortunately, the dynamic properties in the terminal zone are too small to be measured with the present instrument. A modified method is suggested here, which is based on the high frequency part of the spectrum. An expression for the chain size distribution under shear has been proposed by Ruckenstein and Mewis.l6 The present authors have shown the resulting distribution to be identical with the most probable distribution of linear polycondensation reac- t i o n ~ .~ At the same time, evidence was presented that the distribution preserved its shape under changes in shear rate. We can then apply a method, suggested by Menefee17 to calculate the average chain size (by weight) N , from the spectrum height H, at zmin: The viscosities of the dispersions have been measured on a Weissenberg rheogonio- meter. The computational results are represented in table 1. The validity of the TABLE 1 .-CHAIN SIZE N , FOR A CARBON BLACK DISPERSION (c = 2.1 %) AS CALCULATED FROM THE RELAXATION SPECTRA [EQN (5)] 26.2 1.6 1400 6.5 13.1 2.3 1700 8.1 26.2 5.5 2530 14 values obtained for N , should be verified by independent measurements.It has been shown that the carbon black dispersions, which are used here, have structure depend- ent dielectric spectra.'' Electric techniques might therefore be suitable to verify the present chain model. Curves 4 and 5 in fig. 3 correspond to dispersions at rest. At the lower frequencies the real modulus reaches an equilibrium value, which indicates a solid-like behaviour, even at these low concentrations. The behaviour can be explained by the presence of a network structure. The high frequency part of the spectrum is not affected by the presence of a network and preserves its characteristic shape. The difference in level of the spectrum between curves 4 and 5 can be understood on the basis of the number of chains that are present.With more chains, the mesh size will decrease, which will reduce the maximum relaxation time. This effect is also shown clearly in fig. 3. The equilibrium moduli could be used in the usual manner to calculate inter- action forces.lo*ll However, doubling the concentration causes a thirty-fold increase in modulus. As it is difficult to model such changes, the same restriction applies to calculation from the data of concentration-independent parameters for interaction forces. This restriction does not apply to the method suggested above. It is concluded that, at least for certain dispersions, superposition measurements provide more detailed information about the colloidal structure than do the earlier viscosity or elasticity measurements.The technique can be applied to flowing dis- persions and hence does not require the presence of a continuous network structure. The high frequency limit can be related to the interaction forces. In addition a64 MECHANICAL SPECTROSCOPY measure of the chain size distribution is obtained. The technique presented here appears to be a potential tool for measuring characteristics of colloids which are difficult to obtain by other means. The authors are indebted to the Nationaal Fonds voor Wetenschappelij k Onder- zoek and to the Fonds Derde Cyclus (K. U. Leuven) for financial support of this project. One of us (G. S.) acknowledges a scholarship from the N.F.W.O. for the period during which this work was performed. C. J. Nederveen, J. Colloid Sci., 1963, 18, 76. R. D. Hoffman and R. R. Myers, Proc. 4th Int. Congress Rheol., ed. S . Onogi (Interscience, New York, 1965), vol. 2, p. 693. S. Onogi, T. Matsumoto and Y. Warashina, Trans. Soc. Rheol., 1973, 17,47. G. Schoukens and J. Mewis, Trans. SOC. Rheol., 1978, in press. M. Yamamoto, Trans. SOC. Rheol., 1971,15, 331. J. M. Simmons, J. Sci. Instr., 1966, 43, 887. G. Marucci and G. Astarita, Rheol. Acta, 1974,13, 754. J. D. Ferry, Viscoelastic Properties of Polymers (J. Wiley, N.Y., 1961), p. 63. G. Schoukens, PkD. Thesis (K. U. Leuven, 1978). lo M. van den Tempel, J. Colloid Sci., 1961, 16, 284. l1 K. Strenge and H. Sonntag, Colloid Polymer Sci., 1974,252, 133. l2 R. B. Blizard, J. Appl. Phys., 1951,22, 730. l3 B. Gross and R. M. Fuoss, J. Polymer Sci., 1956,19, 39. l4 B. H. Zimm, J. Chem. Phys., 1956,24,269. l5 R. B. Bird, 0. Hassager, R. C. Armstrong and C. F. Curtis, Dynamics of Polymeric Liquids, l6 E. Ruckenstein and J. Mewis, J. Colloid Interface Sci., 1973, 44, 532. l7 E. Menefee, J. Appl. Polymer Sci., 1972, 16,2215. l8 J. Helsen, R. Govaerts, G. Schoukens, J. De Graeuwe and J. Mewis, J. Phys, E., 1978, in press. Kinetic Theory (J. Wiley, New York, 1977), vol. 11, p. 591.

ISSN:0301-7249    

DOI:10.1039/DC9786500058

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Structure and Stability of Concentrated Boehmite Sols BY J. D. F. RAMSAY AND S. R. DAISH Chemistry Division, AERE, Harwell AND C. J. WRIGHT Materials Physics Division, AERE, Harwell Received 7th December, 1977 The viscoelastic properties of dispersions of rnicrocrystalline boehmite (A100H) particles, covering a range of high concentrations (> 10% w/w) and containing different electrolytes, have been measured under oscillatory shear with a Weissenberg rheogoniometer. Stable dispersions were highly elastic and often thixotropic-properties which are ascribed to short range (<lo nm) inter- particle repulsion forces. When destabilised by addition of certain counterions (103-, Br03-, F-, S042-) this elasticity was lost and plastic properties developed. Interparticle repulsion is attributed to extensively solvated polynuclear aluminium cations, formed at the boehmite surface during acid peptisation, whose presence was consistent with quasielastic neutron scattering and other evidence.Light scattering measurements on dilute dispersions (t2% w/w) showed that the latter contain large and very open aggregates of primary sol particles-the number of primary particles per aggregate being dependent on the electrolyte concentration. In more concentrated dispersions (with volume fractions, Q, > 0.1) a stable and coherent structure analogous to the individual aggregates is proposed. In recent years the preparation of stable concentrated (>20% w/w) sols of several metal oxides has been descI5bed.l Such sols, which are composed of small (254 nm to ~ 0 .1 pm) primary particles have been prepared for example by peptisation of hydrous oxide precipitates and fine powders, usually with dilute mineral acids.2 As well as their remarkable stability at such high concentrations, many of these sols have other properties which are not typical of lyophobic colloids. Thus on further concentration they become progressively less fluid (sometimes being thixo- tropic) and are finally transformed into rigid solids, known as " gels ", when the volume fraction of the dispersion, q, exceeds ~ 0 . 4 . Such gels can generally be re- dispersed in water to yield stable sols once again. Indirect evidence, which suggests that the colloidal particles are partially ordered during the transformation of sols to gels has been obtained from gas adsorption studies: which show that many gels have a very uniform porous structure after evacuation.An explanation of some of these exceptional, and hitherto unexplored, features may possibly result from a better understanding of the forces of interaction between the colloidal particles. Accordingly, the stress response of concentrated dispersions of well characterised boehmite particles has been examined under oscillatory shear, with a Weissenberg rheogoniometer. Furthermore, to obtain an insight into the possible role of the water-surface interaction, the quasielastic neutron scattering of water in the dispersions has been measured. Light scattering measurements have also been made on more dilute sols ((2% w/w), to obtain details of possible structure in the concentrated dispersions.66 STABILITY OF CONCENTRATED SOLS EXPERIMENTAL MATERIALS Sols were prepared from a commercially produced (Condea, Petrochemie-Gesellschaft) microcrystalline boehmite powder which was characterised by electron microscopy and X-ray line broadening.The powder consisted of thin ( ~ 4 nm) plate-like particles ~ 2 0 - 30 nm across, and had a specific surface area, SBET, of 190 mz g-l. Concentrated sols were formed by peptising slurries of powder (-10 - 30% w/w) with dilute nitric acid (t0.1 mol dm-3). The minimum amount of acid required for peptisation corresponded to a mole ratio, [HN03]/ [AlOOH], of 2 x 10”; the resulting sol, depending on its concentration, had a pH in the range 3.9 to 4.2. Sols were also examined which had higher mole ratios than 2 x When dried in air at room temperatures, all the sols formed opaque, glassy gels which could be readily redispersed in water to give dispersions of any concentration desired.MI C R 0 EL E C TR 0 P H ORE S I S Electrophoretic mobilities, u, of dilute ( x g cm”) aggregated sols were measured over a range of pH (-3 to 11) with an instrument (Rank Bros., Cambridge) fitted with a capillary cell. LIGHT SCATTERING Concentrated sols (-5 - 20% w/w) were centrifuged (-2 x lo5 m s-~) and light scattering measurements (Sofica, model 42000) were made on diluted samples ( 5 2 x g ~ m - ~ ) at a wavelength of 546 nm using vertically polarised light. Results were treated using the scattering equation based on the Rayleigh-Debye theory : (1) where Re is the Rayleigh ratio corresponding to a scattering angle 8, P(8) is a particle scatter- ing factor, K* is an optical constant, B is the second osmotic virial coefficient and mW is the weight average molecular weight of the dispersed particles of concentration c.The optical K’clRe = (l/Bw)P-l(8) + 2Bc constant is given by: K* = 2n2 fig(d,ii/d~)’A-~ N-I where Ti,, is the refractive index of the dispersion medium, d,ii/dc is the refractive index incre- ment, and 13. and N are respectively the wavelength of incident light and Avogadro’s number. Experimental data were examined using the Zimm plot method4 to obtain ATw, B and the radius of gyration of the particles, R,, by the standard Guinier proced~re.~ OSCILLATORY SHEAR MEASUREMENTS The stress response of dispersions to oscillatory strains ( y = yo sin wt) of progressively increasing peak amplitudes, yo (from z 2 x lo” to 2 x lO-l), was measured with a Weissen- berg rheogoniometer (model R 19; fitted with a cone and plate), within a frequency (2nv = w ) range from z Dispersions (many were thixotropic) were allowed to age for several days and then gently placed on the rheogoniometer platens before making measurements.The response was recorded on a U.V. oscillograph and also analysed vectori- ally (Solartron 1170 frequency response analyser) to obtain storage, G’, and loss, G”, moduli. to lo3 rad s-l. NEUTRON SCATTERING Quasielastic neutron scattering data, obtained with the cold neutron time-of-flight spectrometers (4H5 and 6H) at AERE, Harwell,6 were converted to scattering laws using standard routines.’ The scattering laws were analysed using a simple diffusion model (which holds for pure water when Q2 < 2 A-’),J .D . F . RAMSAY, S . R . DAISH AND C . J . WRIGHT 67 where Q and m are the momentum and energy transfers respectively and F the diffusion constant. S(Q, m) is a Lorentzian function with a FWHM, AE, which is equal to 2hDQ2. D values were then obtained from the limiting slopes at small Q, of plots of AE against Q2. Scattering law half widths were obtained from the FWHM of the experimentally measured quasielastic peaks by deconvoluting their Voigt profiles (using standard tables) and the gaussian instrument resolution curve. Numerical convolution techniques also gave similar half widths. Due to the appreciable number of protons in the boehmite and their associated incoherent scattering, special care was taken to subtract the background scattering from the total produced by the dispersions.RESULTS MICROELECTROPHORESIS Sols were positively charged [u = (4 -I: 0.5)/102 pm s-l V-l m at pH 41, the mobil- ity changing insignificantly in the pH range 253 to 256. At pH > 6, u decreased and an isoelectric point was reached at pH 8 to 9. Measurements at different concentra- tions of potassium nitrate and 10-1 mol dm-3) showed no significant variation. LIGHT SCATTERING Light scattering measurements on diluted samples (<2 x g ~ r n - ~ ) showed that the primary particles in the Concentrated sols formed colloidal aggregates. Aggregation was increased when excess acid was used to peptise the powders and when dilute electrolytes (e.g., KN03, KClQ,, KC104) were added to the sols.For the dispersion corresponding to the Zinim plot shown (fig. l), which was prepared with just sufficient acid to effect peptisation ([HNO3]/[A100H] -2 x the extent I I I I L A 0.4 0.8 1.2 sin2(+) + 14.0 c FIG. 1.-Zimm plot for boehmite sol; [HN03]/[AIOOH] = 2 x Concentrations, CI, Ct, C3, Cq, C,/g ~ r n - ~ are respectively 2.41, 1.93, 1.45, 0.96,0.48, X68 STABILITY OF CONCENTRATED SOLS I I I 1 of aggregation was only limited; it would correspond to 2 to 3 units per aggregate, based on the dimensions of the primary particles obtained from electron microscopy. Data derived from fig. 1 are given in table 1. Results for several other dispersions either prepared with more acid or containing electrolytes are summarised in fig.2 to TABLE LIGHT SCATTERING RESULTS FOR A BOEHMITE SOL Kv R,lm B/mol m3 kg-2 (d2/dc)/rn3 kg-l 1.18 x 107 43, (31)" 1.74 x 10-9 1.04 x 104 * Zero extrapolation of Zimm plot from sin2(8/2) > 0.3. illustrate the extent and variability of aggregation. Larger aggregates were obtained as the concentration of anion in the concentrated sols was increased either during or after peptisation (from 252 x to 2 x 10-1 mol dm-3 for the examples in fig. 2). Measurements, made on diluted samples, withdrawn at intervals after peptisation, showed that the growth of aggregates was initially rapid and then continued more slowly, often for several days, before a stable size was attained; this rate was increased as the boehmite concentration in the concentrated sols (which was normally in the range 1 to 4 mol dm--3) was increased.lo8 i 1, tnm FIG. 2.-Dependence of m,., on R, for aggregated boehmite sols. Broken line shows RJL against XNJeqn (5)] forf = 3. * Refers to a single boehmite particle calculated for dimensions of 25 x 25 x 4nm3.J . D . F . RAMSAY, S . R. DAISH A N D C. J . WRIGHT 69 It can be showng that if logarithmic plots of nw and R,, such as in fig. 2 approach linearity in the limit of high nW (i.e. nW = KR,”), then information on the structure of the aggregates can be obtained from the value of the exponent x. Since the points in fig. 2 fall on a line for which x = 3, the aggregates can be considered to have a structure in which each unit (considered as a mass point) is separated, by a distance L, from f similar units.If the units are arranged in layers, confined by concentric shells having a difference in radii of L, the number of units in each layer being cf - 1) times that of the preceding layer, then the radius of gyration of such an aggregate is given by: Ri = r i N J 3 N, (4) n = l n = l where rn is the distance of the mass points in the nth layer to the centre of gravity and Nn the number of mass points in this layer. Assuming the first “ layer ” contains only one unit, substitution for r, and N,, gives In fig. 2 a plot of R,/L against 237, forf= 3 shows that the experimental data are in satisfactory accord with such a model and, moreover, indicates the low density of the aggregates (viz. L - 30 nm).Additions of some electrolytes (e.g., KF, KI03, KBrO,) at similar concentrations did not, however, give open aggregates, but resulted in destabilisation (uiz. coagula- tion) of sols and rapid sedimentation of boehmite particles. OSCILLATORY SHEAR EXPERIMENTS The effects of progressively increasing strain amplitude, yo, on the storage, G’, and loss, G”, moduli (LO = 99 rad s-l) of boehmite dispersions at several concentra- tions are illustrated in fig. 3. In the lower range of concentration ((32% w/w) sols had viscoelastic properties [cf. fig.3(a)]. As yo was increased however, G’ decreased steadily whereas G” remained almost unchanged-behaviour, which under conditions of steady shear would be consistent with a predominantly viscous fluid. At slightly higher concentrations (33.8 % w/w) the behaviour changed markedly [fig.3(b)]. Thus at low strains the response of the dispersions was almost entirely elastic (G’ 9 G”), until a particular value of yo ( ~ 3 x loA2) was exceeded. A perceptible phase dif- ference between the strain and stress response then began to occur, which corres- ponded to the marked increase in G” and fall of G’ shown; the response still remained linear however. As yo was increased further e 7 x the response became pro- gressively non-linear ; this feature, which coincided with a gradual reduction in peak stress (both G’ and G” decrease), was probably due to the onset of structural break- down in the dispersions. Thereafter G‘ and G” were derived from an analysis of the stress fundamental into the in phase and quadrature components of the strain (ie., neglecting other odd harmonics), a procedure only considered justifiable for yo < 0.15.Measurements of moduli at small strains ( y o = 1.6 x extending to lower fre- quencies showed no significant changes for LO > 1 rad s-l (fig. 4). Below this fre- quency a gradual increase in G” occurred which probably reflected the onset of structural relaxation. The dependence of the initial storage modulus, G;O+O, on concentration, is compared for other types of boehmite dispersion in fig. 5. An important feature is70 STABILITY OF CONCENTRATED SOLS N ‘E 0 m e c VI I 10” lo-* lo-’ 1.0 strain amplitude, Yo FIG. 3.-Dynamic shear moduli, G’, G” of boehmite dispersions ([HN03]/[A100H] = 2 X at different strain amplitudes, yo (a = 99.3 rad s-I). Concentrations, boehmite % w/w, (a) 31.9, (b) 33.8, (c) 37.1, ( d ) 42.6, (e) 49.0.Solid symbols denote G”, open symbols G’. radial frequency, w/ rad s-’ FIG. 4.-Storage and loss moduli of boehmite dispersion (34% w/w) at different test frequencies, ~ ( 7 0 = 1.19 x lov2). [NO~]/[AIOOH] = 4.2 X 10”. (0) G’, (a) G”. the marked rise in G;o-+o which results from an increase in the mole ratio of nitric acid (from 2 x to 4 x loA2) used for peptisation [cf. fig. 5(a) and (b)]. This effect, which was most striking at lower dispersion concentrations, was apparently due to the increase in the nitrate ion concentration, because additions of KNO, solution to sols peptised at low acid ratios had a similar effect [fig. 5(c)]. Extensive disruption of the dispersions under oscillatory shear began at a strain (yc 2 6 x which corresponded to a maximum in peak stress ad in phase withJ .D. F. RAMSAY, S . R . D A I S H A N D C. J . W R I G H T lo4- P) lE lo3- 7 \ ruu p lo2- 0) In z .- " 10 c;' Y E , I 1- - I l a volume fraction, Ib 0.1 0.2 a3 1 I I / b t 0 71 ** 1.2 1.L 1.6 1 .a log m.( % "W FIG. 5.--Storage moduli, G$o+o, of boehmite dispersions at different concentrations. [HN03]/- [AlOOH]: (a), 2 x (c) [NO?] = 0.4 mol dm-3, [HN03]/[A1001-I] = 2 X lo-'. (b), 4 x n.b. ro = 99 rad s-'. the strain. The work required to disrupt the dispersions, equivalent to their cohesive energy, E,, is therefore given by: E, = /I a'dy. Values of E, increased markedly with increases in dispersion concentration (fig.6)72 STABILITY OF CONCENTRATED SOLS and were also enhanced on further additions of both nitric acid and potassium nitrate solutions. Study of the effects of electrolyte concentration at a fixed dispersion concentration (28% w/w; [HNO,]/[ALOOH] = 2 x 1W2) showed that a similar and progressive increase in E, occurred with KNO,, KClO, and KC10, (e.g., E, w 6 and ~ 2 7 J me3 at 5 x and lo-' mol dm-3, respectively) up to ~ 0 . 1 5 mol drn-,; thereafter (up to w0.4 mol drn-,) little further change took place. Solutions of KI03, KF, K2S04, of low Concentration ( ( 5 x mol dm-3) also produced initial increases in G' and E,, but thereafter, on further increases in concentration, the dispersions lost their elasticity and developed plastic properties. This was typified by a marked non- linearity in the stress response, which contained significant contributions from the third and fifth harmonics, and approached a square wave.Eventually ([anion] > TABLE 2.-cONCENTRATiONS OF POTASSIUM IODATE SOLUTIONS REQUIRED TO DESTABILISE BOEHMITE SOLS* boehmite KI03 conc. (% w/w) conc./mol dm-3 [103]/[AlOOH] 11.7 0.04 2.0 x 20.8 0.08 2.0 x 27.9 0.12 1.8 x 33.8 0.15 1.6 x * [HNOJ[AlOOH] = 2.0 X 10-1 mol dm-3) sedimentation occurred due to a coagulation of the sol particles. Similar effects were observed with KBrO, solutions at higher concentrations (20.3 mol dm-3). The concentration of electrolyte (KI03, KF, KBrO,) required for destabilisation (i.e., to cause rapid sedimentation) was dependent on the dispersion concentration, as is illustrated for KIO, solutions in table 2.It will be noted that at the point of instability, the ratio [IO;]/[AlOOH] is close to the mole ratio of peptising acid. QUASI-ELASTIC NEUTRON SCATTERING Scattering law half widths, AE, for dispersions of several concentrations (at 296 K) are plotted in fig. 7 as a function of the square of momentum transfer, Q2 (a plot at 49% w/w has been omitted for the sake of clarity). Diffusion coefficients of water, D, obtained from the limiting slopes of these plots (table 3), decrease progressively as the dispersion concentration is increased. In contrast, for a concentrated (55% w/w) paste of unpeptised boehmite powder, D was very similar to that of bulk water. As Q increases, and the diffusion event is observed on a diminishing time scale ( Z 10-l1 - lo-', s), the curves deviate from the limiting slope, an effect which is most marked for the highest concentration.This feature has been ascribed'' to the water diffusion becoming less continuous and more like jump diffusion, since then whereJ . D . F . RAMSAY, S . R . DAISH A N D C. J . WRIGHT 73 0 1 2 3 lI2/ FIG. 7.-Dependence of quasi-elastic scattering, aE, on square of momentum transfer, Q2, for boehmite dispersions of different concentration, % wlw, (a) 28, (b) 34, (c) 43, (d) 52. where zo is the mean time between jumps of length 1. Further analysis on the basis of this model is unfortunately precluded until the contribution of rotational diffusion to the scattering is known. The present calculations of D are, however, valid because it has been shown that such a contribution becomes insignificant at low Q.lf TABLE 3.-DIFFUSION CONSTANTS, D, OF WATER IN BOEHMITE DISPERSIONS DERIVED FROM QUASI-ELASTIC NEUTRON SCATTERING MEASUREMENTS dispersion conc.(% wlw) (P D x 109/m2s-l water - 2.14 28 8.0 x 2.02 34 1.45 x 10-l 1.83 43 1.99 x 10-1 1.67 49 2 . 4 3 x 10-1 1.38 52 2.69 x 10-1 1.07 55 * 2.92 x 10-1 2.27 _ ~ _ ~ ~ * Paste of unpeptised boehmite powder. DISCUSSION Many of the properties of the dispersions can be ascribed to a short range (< 10 nm) interparticle repulsion which is different from the electrostatic repulsion encountered with lyophobic colloids. This interpretation is required by the presence of the open aggregates of particles observed by light scattering. These increase in size as the anion concentration in the dispersions is increased (> 10-1 mol dm-3) and the electro- static repulsion becomes negligible, resulting in a loosely flocculated network, whose structure is determined by a balance between van der Waals attraction (VA) and a short range repulsion.If at higher concentrations than those normally employed for light scattering (q7 > a similar but coherent network extends throughout the74 STABILITY OF CONCENTRATED SOLS dispersions, then the cohesive energies, E,, will be related to the work required to disrupt the network, which in turn will reflect the depth of a P.E. minimum resulting from attraction and repulsion interactions. In table 4 the interaction energy per particle of boehmite, e,, has been estimated from E, at different dispersion concentra- tions by assuming a number concentration, N, based on a particle volume derived TABLE 4.-cOHESIVE ENERGIES, E,, OF BOEHMITE DISPERSIONS AND VAN DER WAALS INTERACTION, v ~ , BETWEEN PARTICLES dispersion conc. e, x 1021/J (% wlw) P EJJ m-3 per particle (VAs)* x 1OZ1/J t/nm 33.7 1.45 x lo-' 2.05 x 10 3.53 x 10-1 2.00 10.0 37.1 1.65 x 10-1 3.00 x 10 4.54 x 10-1 2.62 9.2 40.1 1.82 x 10-1 1.52 x lo2 2.09 3.38 8.5 42.7 2.00 x 10-1 2.74 x lo2 3.42 4.38 7.8 49.0 2.43 x 10-1 1.42 x lo3 1.46 x 10 8.13 6.2 * Area of interaction per particle, s, is 6.25 x m2.n.b. [HN03]/[A100H] = 2 x from electron microscopy (uiz. 4 x 25 x 25 nm3). At lower concentrations, where the dispersions exhibit thixotropic behaviour, e, is comparable with kT (4 x J), a feature which probably indicates the beginning of a continuous structure due to association of aggregates.Values of e, at different dispersion concentrations can be compared with calculations of VA for a pair of parallel boehmite particles, of thickness 6, if a hypothetical structure is assumed in which all the particles are arranged in cubic close packed arrays and are separated on all sides by a distance t, where V, is given by12 A VA = - 4s [(t/2)" + (t/2 + s)-2 - 2(t/2 + S/2)-". (9) Values of Va (table 4) calculated with a Hamaker constant, A , of 4.2 x J, as reported for alumina in water,13 and 6 of 4 nm, are in better agreement with e, as the dispersion concentration is increased, which possibly suggests that the particles become more aligned as their separation is decreased. This arrangement would be consistent with the properties of the dispersible boehmite gels,14 which contain slit- shaped pores of width ~4 nm.Using a somewhat similar approach to that previously employed for other col- loidal dispersions l5 having elastic properties, the magnitude of the interparticle repulsion, PR, can also be estimated in principle from the dependence of G& on dispersion concentration, if the separation and arrangement of the particles is known with some confidence. Although such estimates can only be tentative because the arrangement of the boehmite particles is uncertain, calculations based on the hypo- thetical structure described show that PR rises rapidly and far exceeds the van der Waals attraction, V,, when p > 2 x lO-l, a feature which accords with the lyophilic properties and stability of the concentrated dispersions.A possible reason for this short range repulsion could arise from the presence of polymeric aluminium cations, which are formed at the surface of boehmite particles during peptisation with dilute nitric acid. These would be similar to the polynuclear ions, present in solutions of partially hydrolysed aluminium salt solutions, which have indeed been reported 1 6 9 1 7 to be highly effective in stabilising lyophobic colloids such as polymer latices. Adsorption at the colloid surface has been shown to beJ . D . F . RAMSAY, S . R . DAISH AND C . J . WRIGHT 75 particularly enhanced17 with the more extensively hydrolysed ions [e.g., Al,(OH)ii, A11304(0H)72i], which would be expectedls at the relatively high pH (>3.7) of the boehmite sols.In the present case, however, it is possible that the ions remain chemic- ally bound to the underlying boehmite after peptisation of a surface layer. Although the surface concentration of polynuclear cations required for stabilisation is evidently quite low (viz. one cation per 7 nm2, assuming one mol of Al,,O,(OH)\$ is formed for every 7 mol of HN03 added) the amount of water associated with each ion in solution is probably considerable. The presence of the polynuclear ions on the surrounding water probably contributes to the progressive reduction in the diffusion constant, D, as the dispersion concentration is increased-an effect, which although more marked, has been reportedl1*l9 for concentrated electrolytes, containing other " structure promoting " cations (e.g., Li+, Mg2+, Ca2+). Reductions in the diffusion constant of water in dispersions of ultrafine fumed silica powders of similar concentration have been reportedlo to be of similar magnitude to those found here.This effect has been ascribed to a structuring of water promoted by the silica surface. However, under the preparative conditions which were em- ployed it is likely that the silica surface was covered with a layer of polysilicic acid20 and that a similar mechanism for a reduction in D to that discussed for boehmite dispersions could also be appropriate. The stabilising role of polynuclear ions at the boehmite surface is also consistent with the powerful coagulating effects of anions, such as IO;, Br03, F- and SO$-, which form insoluble complexes with hydrolysed aluminium ions,21 e.g., Na [Al,,04(OH)2,(H,0)12(S04)4].Since most metal ions of valency +3 and +4 readily hydrolyse in solution to give polynuclear ions, the stabilising mechanism discussed here may also apply to a wide range of other concen- trated metal oxide sols, which have lyophilic properties typical of those described for boehmite. We thank Mr. R. G. Avery and Mr. G. H. Hearn for experimental assistance in part of this work. R. M. Dell, 7th International Symposium on the Reactivity of Solids, ed. J. S . Anderson et al. (Chapman and Hall, London, 1972), p. 553. C. J. Hardy, Sol-gel Processes for Ceramic Nuclear Fuels (IAEA, Vienna, 1968), p. 33. J. D. F. Ramsay, Chromatography of Synthetic and Biological Polymers, ed. R. Epton (Ellis Horwood, Chichester, 1977), p. 339. B. H. Zimm, J. Chem. Phys., 1948,16,1093. A. Guinier, Ann. Phys. (Paris), 1939, 12, 161. London, 1970). A. H. Baston, UKAEA Report AERE-M 2570 (HMSO, London, 1972). R. Kratochvil, P. Munk and B. SedliEek, Coll. Czech. Chem. Comrn., 1962,27, 115. ti L. J. Bunce, D. H. C. Harris and G. C. Stirling, UKAEA Report AERE-R 6246 (HMSO, a J. Tudor-Davies and J. M. Vaughan, Astrophys J., 1963, 137, 1302. lo R. G. W. Anderson and J. W. White, Spec. Disc. Faraday SOC., 1970, 1,205. l1 J. W. White, Ber. Bunsenges. phys. Chem., 1971, 75, 379. l2 J. Th. G. Overbeek, Colloid Science, ed. H. R. Kruyt (Elsevier, Amsterdam, 1952), vol. 1, l3 J. Visser, Adv. Colloid Interface Sci., 1972, 3, 331. l4 R. G. Avery and J. D. F. Ramsay, unpublished work. is J. W. Goodwin and R. W. Smith, Disc. Faraday SOC., 1974,57, 126. l6 E. MatijeviC, S. Kratohvil and L. J. Stryker, Disc. Faraday SOC., 1966, 42, 187. l7 E. MatijeviC, J. Colloid Interface Sci., 1977, 58, 374. l9 G. J. Safford and P. S. Leung, Ber. Bunsenges. phys. Chem., 1971, 75, 366. 2i G. Johansson, Acta Chem. Scand., 1960, 14, 771. p. 267. See, for example, J. H. Paterson and S. Y. Tyree, J. Colloid Interface Sci., 1973, 43, 389. J. A. Kitchener, Disc. Faraday SOC., 1971,52, 379.

ISSN:0301-7249    

DOI:10.1039/DC9786500065

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Neutron Scattering From Colloids BY DERYCK J. CEBULA AND ROBERT K. THOMAS Physical Chemistry Laboratory South Parks Road, Oxford NICHOLAS M. HARRIS, JAMES TABONY AND JOHN W. WHITE* Institut Laue-Langevin 156X, 38042 Grenoble Cedex, France Received 15th February, 1978 This paper appraises the usefulness of neutron diffraction and small angle scattering for determin- ing the structure of dilute and concentrated sols. For monodisperse polystyrene latex, the particle size and density can be readily determined and an upper limit to density fluctuations within the colloid partide set. For the polystyrene latex peptized by the adsorption of laurate, the physical dimensions and packing density of the adsorbed phase can be determined. The effects of polydisper- sity for unpeptized and peptized graphite sols, and the effects of extreme particle anisotropy using sols of montmorillonite clay minerals have been studied.The chief advantage of neutron scattering for the study of adsorption at the solid- liquid interface, and in particular of colloidal dispersions lies in the fact that by vary- ing the hydrogen to deuterium ratio in the supporting solvent, scattering from the supporting colloid particle may be contrast-matched out of the scattering pattern, thereby leaving the information from the adsorbed layer with high signal to noise. When this is coupled with the fact that the neutron wavelength may be varied widely to avoid Bragg scattering effects inside the colloidal particles, and that the range of particle sizes readily observed by low angle neutron diffraction lies between a few Bngstrom and ~ ~ 4 0 0 0 Angstrom, we see that there may be some distinct advantages to the method.Neutron methods have now been extensively used in metallurgy and in glass and ceramics technology for the study of precipitation and defect structures,l as well as more recently in the study of biological macromolecules and assemblies.2 All of these studies have rested strongly on this phenomenon of variable contrast. Neutrons are scattered predominantly by the interaction of the neutron with the nuclei in the sample material. This interaction occurs at extremely short range (typically 10-l5m) as expressed by the delta function in the potential energy of inter- action V(r) [eqn (l)] bi 6(R - Rf). 271h V(r) = - m The intensity of the interaction is determined by the nuclear scattering length bi, and m is the neutron mass.The intensity of scattering is proportional to the square of the scattering length bl. For small angle scattering, when the momentum transfer in the scattering event is much smaller than the inverse of the particle size, an average scattering length may be used for molecular substances which is simply the sum of the * All communications should be addressed to Dr. J. W. White.D . CEBIfLA, R . K . THOMAS, N. M. HARRIS, J . TABONY, J . W. WHITE 77 scattering lengths of the separate nuclei in each molecule. From this, one can con- struct an average scattering length density knowing the number of molecules and the volume of the scattering particle. Scattering lengths and scattering length densities of the different materials making up the colloid particles in our studies are shown in table 1 as well as those for H20 and D20.If we define the object of interest in a scattering experiment in terms of its scatter- ing length density distribution, p(R) then the distribution of scattered intensity for neutrons, is directly related to the Fourier transform of this distribution: I(Q) = (IA(Q)I~> = (1 P(R)~XP(~Q- m3~i2) (2) V where Q is the momentum transfer in the scattering experiment defined by A(Q) is called the structure factor and A is the incident neutron wavelength. Eqn (2) gives the intensity distribution expected for an isolated particle surrounded by a vacuum. For the expression to be useful, in practice, the sample must be sufficiently dilute so that the observed scattering comes only from individual particles. Addi- tionally, for particles surrounded by a continuous medium, it is the difference in scattering density between the particle and the medium which determines the intensity of scattering, and so in eqn (2), we must replace p(R) by (p(R) - p,), where pb is the scattering length density of the medium.The systematic observation of I ( Q ) as a function of p, constitutes the " contrast variation " technique described later on. In general, approximations to eqn (2) are required to enable the scattering patterns to be analysed. The most widely employed is the Guinier approximation3 shown in eqn (4): I(Q) = I(0) exp -J&Q2 (4) where I(0) is the intensity at zero momentum transfer, Rg2 is the radius of gyration of the particle defined by with V the particle voIume and pm the mean scattering length density of the particle defined by (6) Pm = yl,P(R)d3R. 1 This approximation is valid at low values of the momentum transfer, Q, (QR, < 1).The Guinier approximation may apply for uniform particles of any shape, where- upon a (In I(Q), Q2) plot gives a straight line whose slope is -R:/3. For homo- geneous particles the radius of gyration is the same as the normal mechanical radius of gyration and so the particle dimensions can be calculated for particles of a given form. In cases where the density distribution has higher moments than the second, the contrast variation method can lead to further information: the method has been extensively developed by St~hrmann.~78 NEUTRON SCATTERING FROM COLLOIDS CONTRAST VARIATION METHOD For a non-homogeneous monodispersed sol at small Q, the Guinier approxima- tion applies and it can be shown that as a result of the density distribution in the particle, the radius of gyration depends upon the contrast.This is in clear distinction to the case for a uniform particle, where R,Z is independent of the contrast between the scattering particle and the surrounding medium. Eqn (5) becomes where pf(R) = p(R) - pm and p , the contrast is defined by P” Pm - ~ s - (8) R,2“ is the previously defined radius of gyration for a homogeneous particle with the mean scattering length density, and may be determined experimentally by plotting the values of R,2 obtained from Guinier plots against l/p.At l/p’ = 0 effective contrast is infinite and gives the value of RZv. Conversely, the term arising from the variation of scattering density with radius inside the particle dominates the scattering as the contrast approaches zero. To find p’ from eqn (8) we need to know pm, which is measured experimentally by observing the contrast behaviour of I(0). At zero scattering angle (Q = 0) the expo- nential in eqn (2) becomes unity, and one readily sees that I(0) = [pmV]2 = [CbiI2. (9) I(0) is thus independent of the particle geometry and density distribution, but depends upon constituent atoms forming the particle. Thus the adsorption on to a colloid particle can be readily measured by the changes in I(0). Since, in contrast variation I(0) is given by = (PmV - psQ2 (10) = (C bi - ps V)’ (1 1) then the intensity of scattering is zero when pm = ps.This immediately fixes the mean scattering length density pm, which is found by plotting m) against ps. The slope of this plot also gives the particle volume, V, if the values of intensity are normalised to absolute units (em2). This can be done by calibrating the intensities of scattering against a water standard (which scatters isotropically) or by a direct comparison with particles of known volume. When the molecular compositions of the substrate and the adsorbate are known, then the number of molecules of adsorbate per particle can be determined. Spherically symmetrical particles give rise to maxima in the scattering pattern at higher Q, which are experimentally observable for monodisperse systems.These correspond to the Bessel function maxima given by the analytical solution of eqn (2), p(R) being scalar in this case. For homogeneous spherical particles @(R) = pm), this gives In general, eqn (2) can be inverted, thereby enabling p(R) to be calculated directly from Z(Q) for monodispersed spherical systems. This technique has been used toD. CEBULA, R . I<. THOMAS, N. M. HARRIS, J. TABONY, J . W. WHITE 79 study density inhomogeneities in swelled polystyrene latex and promises to give infor- mation on the swelling process when styrene is added to preformed latex. By intro- ducing deuterated styrene monomer during swelling, a '' tracer " of high scattering length density is created (see table 1).TABLE SUR VALUES OF SCATTERING LENGTHS PER ATOM bi OR TOTAL SCATTERING LENGTHS PER MOLECULE &hi OF VARIOUS SUBSTANCES, AND THEIR CORRESPONDING SCATTERING LENGTH DENSITIES p AT (MASS) DENSITY CT b, or 0 P &bi/cm x /g ~ 1 1 - r ~ /crnc~n-~ x 10'' hydrogen deuterium H20 3 3 2 0 H-pol ystyrene D-polystyrene H-laurate D-laurate carbon montmorillonite -0.374 $0.667 -0.168 1.914 2.33 10.66 0.538 24.481 0.665 18.4 1 .oo 1.10 1.05 1.13 0.8 0.8 2.0 1.3 - 0.56 6.36 1.41 6.48 0.1 3 5.3 6.7 3.8 Suitable highly spherical monodispersed particles (e.g., latex) can also be used as a substrate for adsorption to give spherically symmetrical adsorbed layers. This enables the above technique to be used to study the density structure of these adsorbed layers. By again using hydrogen-deuterium substitution, features of the adsorbed layer can be " highlighted ".Contrast variation techniques with 2/I(O) and R,2 analysis can also be applied to these systems to yield accurate values of layer density, thickness and the surface per adsorbed molecule. I(0) can be evaluated either by Guinier extrapolation [eqn (4)] or (more accurately) by fitting the observed scattering to an equation of the form of eqn (12). The accuracy of these measurements is, however, very sensitive to sample polydispersity, as is reflected in the results of the experiment on the sodium laurate + latex system reported below. For colloidal particles which are ellipsoids, cylinders or platelets, measurements of the radius of gyration is not sufficient to describe the particle shape.For the simplest case of homogeneous particles, forms of the scattering function I@) can be derived for fitting to the observations. For the case of narrow cylinders (radius R and height H) we have: I(Q> (l/QH> ~xP(- Q2R2/4) (1 3) and for thin discs we have : I(Q) cc (1/Q2R2) exp(-Q2H2/12) (14) which are valid for QH < 1 and for QR > 1. A further approximation is valid for high Q (QH > 1 ) namely Porod's law whereupon It can be readily imagined that for non-uniform particles such as platelets with surfactants adsorbed at the interface, the scattering law would be strongly modified80 NEUTRON SCATTERING FROM COLLOIDS and that contrast variation techniques as used for the spherically symmetrical colloids above reveal many details of the texture of the adsorbed layers.A particularly interesting case is for clay platelets whose thickness may be of the order of 10 A and whose extension may be of the order of 1000 A. By adsorbing suitable partly deuter- ated molecules, the conditions under which the concept of a mean scattering length density is applicable in the direction perpendicular to the sheet can be made to break down leading, uniquely, to structural information in this direction. EXPERIMENTAL Polystyrene latices containing a single ionogenic surface species (carboxylic acid groups), and with a small coefficient of variation in the particle size (typically a few percent), have been prepared by Ottewill and his collaborator~~~~ as model colloids. Samples of this material, RB66 in stabilised dispersion at 0.19% weight per volume, and in aqueous mixtures contain- ing between 0%-60% D20 at pH 9.8 were used for the neutron scattering measurements.The mean bead diameter determined by electron microscopy was 462 A with a coefficient of variation of 19%. For these experiments the samples were contained in silica sample cells and small angle scattering was measured with 10 A neutrons at the 20 m position of the D11 small angle scattering machine in Grenoble. Acceptable statistics for high contrast samples were obtained in 2 h counting times, and spectra were taken for seven D20 concentrations and blanks. The density of the polystyrene was quoted as 1.058 g ~ r n - ~ giving a contrast matchpoint in H20 + D20 mixtures at 29% DzO: 71% H20. All measurements were made at room temperature of 25 k 1°C.The pH of the samples was maintained at pH = 9.6 to ensure the solution stability. A similar experiment was performed on samples of the latex with an adsorbed monolayer of laurate ions, following an isotherm for the laurate ion on latex determined by Ottewill et aL6 Solutions of sodium laurate (dodecanoate) were prepared from lauric acid by reaction with sodium hydroxide (AnalaR grade) for both the normal and the deuterium labelled acids. The latter was obtained from Merck, Sharpe and Dohme as lauric acid D-23 Ref. MD 1234 Lot no. B 820 of isotopic purity 98%. The protonated lauric acid was Merck Ref. 5339. Excess sodium hydroxide was added to raise the pH to 9.2 for the stock solutions of molarity 0.3. The concentration of laurate ions in the sample was 2 x 10-2mol md-2, chosen to give mono-layer adsorption and being below the critical rnicelle concentration (= 2.8 x mol- dme3).Ionic strength of solutions was raised by addition of NaCl to loe2 mol dm--3. Samples and blanks were made up at latex concentration 0.19% wt/vol. in the H20/D20 mixtures containing 0,20,29, 37, 50 and 56% D20. A sample of latex in H20 without sur- factant was also included for calibration, and direct beam attenuation measured for each sample to determine sample self-absorption. The graphite, a sample of Vulcan I11 batch no. 2A/29 surface area 71 m2 g-l, obtained from the National Physical Laboratory, Teddington, U.K. was ultrasonically dispersed in mixtures of D20 and H20. Dispersions with concentrations of 0.2 to 10% by weight carbon were sonicated for 90 s each using an ultrasonic finger in direct contact with the solution.This time was rather less than the five minutes specified by Medalia and Heckman for com- plete dispersion of the graphon aggregate^.^ To one group of samples was added 35 mg of sodium dodecyl sulphate per 100 mg of carbon, equivalent to 5 monolayers if the surfactant molecules occupy an area of 50 A2.8 This S.D.S. concentration ratio was kept constant. The peptised samples were noticeably more stable than the dispersions in water, remaining apparently dispersed for several months. Some of the unpeptised samples, particularly at high carbon concentration, were observed to have largely flocculated even during experi- mental runs (i.e. up to 3 h after dispersion).Electron micrographs of the diluted peptised suspension were taken and showed that, even in the apparently dispersed solution, clusters of graphon particles existed. Since further sonication is known to cause oxidationg this was not at tempted. For the experiments on clay platelets, the raw clay mineral used was bentonite (NumberD. CEBULA, R. K . THOMAS, N. M. HARRIS, J . TABONY, J . W. WHITE 81 1 - 26) from Clayspur, Wyoming (API Clay Minerals Standard Project 49). Standard techni- ques described elsewhere by Callaghan and Ottewill10 were used to remove residual organic compounds and traces of undersirable heavy metal cations. The clay was exchanged with lithium, sodium, potassiumA and caesium ions for the separate studies and thoroughly dialysed before use.Three separate volume fractions of clay below 2% were studied for each species. All measurements were made at a laboratory temperature of 25"C, using the D11 small angle neutron scattering camera of the Institut Laue-Langevin, Grenoble, at momentum transfers between and 10-1 A-1. The attenuation of the undeviated beamwasmeasured to enable the sample self absorption corrections to be made for all cases. a a 0 0 r J r 3 0 O El a RESULTS POLYSTYRENE LATICES Guinier plots of the small angle scattering from unpeptized polystyrene latex particles suspended in various mixtures of H20 and D20 are shown in fig. 1. Except near the contrast matching point (325% D20) good straight line portions are obtained whose slopes immediately give the radius of gyration R,v, R, = 172 & 7 A.Since, for spheres, the radius of gyration RgV2 is equal to 0.6 R2, where R is the radius of the sphere, neutron scattering measurements lead to a sphere radius of 222 & 9 A, which agrees well with the value of 231 A determined by electron microscopy? The slope of the Guinier plots is independent of the contrast within the accuracy of the measurement and, therefore, we conclude that the gradient of the scattering density within the particle is very small. At very low values of momentum transfer (Q2 < 7 .v 2 4 )-. c - 8 3 C - tAYAAAAA 2 1 A A A A82 NEUTRON SCATTERING FROM COLLOIDS 10 x A-2), slight curvature of the Guinier plots indicates presence of some large particles possibly arising from flocculation. The dependence of the extrapolated intensity at zero angle of scattering upon the scattering length density of the surrounding solvent (and hence the contrast) is shown LO 20 h 0 i t cr U c c A 0 .- w 0) CT II 4- .- 2O-20 I=" -40 FIG.2.-Square root of the intensity at zero scattering angle as a function of the scattering length density of the surrounding solvent for polystyrene latex particles. in fig. 2. length density, pm, From the contrast matching point [eqn (9) and (lo)] the mean scattcriiig pm = 1.41 & 0.05 x 1010crn-2. Since the mass density, CT, is related to the scattering length density by where M - is the molecular weight of the poystyrene subunit, (CbJ, is the total scatter- ing length of these molecules and N is Avogadro's number. This leads immediately to a mass density of 1.05 & 0.04 ~ r n - ~ , which is in good agreement with 1.057 ~ r n - ~ quoted by 0ttewill.ll SUBSTRATE WITH ADSORBED MONOLAYERS OF PROTONATED AND DEUTERATED LAURATE The same polystyrene latex as measured above and after ageing for about 4 months, was used for these measurements. The Guinier plots of the low angle neutron scat- tering intensity as a function of the squared momentum transfer are shown in fig.3(a) and (b) for adsorbed protonated lauric acid and adsorbed fully deuterated lauric acid respectively. Patterns at four different contrasts for the protonated laurate and two different contrasts for the deuterated laurate were observed; the pattern for the latexD . CEBULA, R . K. THOMAS, N. M. HARRIS, J . TABONY, J . W . WHITE 83 FIG.3.-Guinier plots of polystyrene latex particles with adsorbed protonated and deuterated sodium laurate in different contrast media. (a) Latex with an adsorbed monolayer of protonated laurate in (i) 0% D20; (ii) 37% DzO; (iii) 50% DzO; (iv) 56% D20. (b) Latex with an adsorbed monolayer of deuterated laurate in (v) 37% DzO (contrast match!); (vi) 50% DzO; (vii) 56% DzO. (c) Latex in Cviii) 0% DzO.84 NEUTRON SCATTERING FROM COLLOIDS alone supported in pure H20 was measured for comparison with the previous results Looking at the low angle scattering pattern for the latex particles alone, it is evident that some flocculation has occurred during the ageing period, leading to a considerable increase in scattering at small angles (Q2 < 0.5 x lo-' A-z); the Guinier region is thus obscured.Using the approximately linear higher momentum transfer region of this curve, the radius of gyration for the latex alone was found to be R, = 165 & 8 A in comparison with R, = 172 rt 7 A determined from the previous experiment where measurements were made at much lower angles. The relatively low accuracy of these measurements (-5%) is due to the random instrumental errors and the more systematic errors affecting the validity of the Guinier approximation, e.g., polydispersity. Both these are much reduced when one con- siders relative values obtained in experiments using the same latex sample. We thus assume a substrate particle radius of 213 A for the further analysis (= R, = 165 A). We also assume that the substrate particles have not suffered actual dimensional changes with ageing, i.e.the density is as previously measured, and pm = 1.41 x lO1O cm-2. The need for these assumptions and the high error on particle size will be eliminated in future measurements, the size of the particle being determined by observation of the full scattering curve, including several subsidiary maxima. The calculated depend- ence of scattered intensity with momentum transfer for latex with an adsorbed laurate monolayer at different values of the contrast is given in fig. 4. This clearly shows the subsidiary maxima and the effect of contrast on the scattering from such a system. The shape of the equivalent pattern given by bare latex (i.e. homogeneous particles) is contrast-invariant. [fig. 3(4i. 8 1 1 FIG.4.Variation of scattered intensity with momentum transfer (8) as calculated using relations of the form of eqn (12) for a uniform particle of radius 222 A, and of scattering length density 1.41 x 1Olo cmV2 surrounded by a layer of thickness 14 A of scattering length density 0.1 x 1O'O cm-2. 4 differ- ent values of contrast ps are shown. - ,0.5 x lolo; ---- , 1.0 x 1010; --- . , 1.5 x 1OlD; . . . . . .2.0 x 1O1O cm-2. pm = 1.16 x loio cmV2.D . CEBULA, R . K . THOMAS, N . M. HARRIS, J . TABONY, J . W . WHITE 85 The clear downward trend in the curves in fig. 3 above Q = 3 x is due to the first minimum in the diffraction curves (cf. fig. 4). Fig. 5 shows a variation in the square root of the intensity at the zero scattering angle as a function of the scattering density of the solvent for the low angle scattering patterns shown in fig.3. Since linear behaviour can be assumed [eqn (9)], the line associated with the adsorbed protonated laurate on the latex is fairly well defined by four points. The points obtained from the deuterated system must lie on a line parallel to this, as shown, even though there are only three points. The line for the latex only has been defined from the measured value of l/I(O) at zero percent D,O and x C .- Y +' -20. -30 -401 FIG. vent 5.-Dependence of the square root of the scattering intensity at zero angle scattering on the sol- scattering length density : A-latex plus deuterated laurate, B-latex plus protonated laurate, C-latex alone, by the contrast matching point assuming a particle density of 1.05 g cm3, (i.e.pm = p s = 1.41 x cm-2). In drawing the straight lines A and B of fig. 5, it has been tacitly assumed that the conformations of the adsorbed laurate ion for the deuterated and protonated molecule are the same. The ratio of the slope of the lines A and B to that of C gives the volume ratio for the adsorbed and free latex particles, leading to an average thickness for the laurate ion layer of 10 & 5 A. From the intercept on the ps axis, the mean scattering length densities for the com- posite particles and for the bare latex particle can be determined. The value pms is the volume weighted mean of the substrate and surfactant scattering densities p,' and p,"' respectively, t y / + p,"' VI" p," = V" where V" = V' + V"'. With the known volumes of the two parts of the particle, the scattering length density of the adsorbate, p,"' is immediately determined. Since the mean scattering intensity per molecule of adsorbed laurate is known, the number of laurate molecules in the adsorbed layer follows immediately and hence the surface area occupied by the laurate molecule.Using a specific surface of latex calculated from the particle geometry, the parameters determined in this way are listed in table 2.86 NEUTRON SCATTERING FROM COLLOIDS It is interesting to note that the area occupied by one laurate ion is 48 & 6 A2, which compares well with the values determined by classical adsorption isotherms.6 This number is fairly insensitive to the latex diameter, because of the relatively large volume of the adsorbate layer with respect to the bare polystyrene sphere.TABLE 2.-PmMETERS OBTAINED FROM THE VARIATION OF l/l(o) WITH CONTRAST (FIG. 5) OF LATEX WITH AN ADSORBED MONOLAYER OF LAURATE. laurate ion thickness lOA5A protonated laurate scattering density deuterated laurate scattering density no. of laurate ions adsorbed per particle surface per laurate ion density of laurate layer 0.1 & 0.1 x 1O1O cm-2 4.8 & 0.7 x lolo cm-2 1.2 & 0.2 x lo4 48 & 6 A2 0.72 & 0.1 g cm-3 Some check on the self-consistency of these analyses is given first by the inter- section of lines C and B of fig. 5, which gives the scattering length density of the deutero-laurate layer alone pm”’ = 4.4 & 1 x 1O1O cm-2. This is in agreement with the value calculated from the total mean scattering length density for the particle, pm”, calculated from the intercept of line A with the abscissa. Eqn (16) gives the density for the laurate ion in the adsorbed layer as 0.72 & 0.1 ~ m - ~ .An independent check of these values is given by the variation of R,2 with the reciprocal of the contrast. This variation for the protonated and deuterated laurate systems is shown in fig. 6 . From eqn (7) the radius of gyration of the equivalent homogeneous particle, given by the intercept is R,v = 180 & 5 A. This gives the total radius of the composite particle as R = 232 & 6 A which when compared with R = 213 & 6 A for the bare particle indicates a layer thickness of 19 & 12 A. The slope of the lines is given by the second moment of the scattering length den- 2 4 - 1.0 - 0.5 C I 0.5 (contrast)-’ / 10’0 cm* FIG.6.-Variation of the mean square radius of gyration, R,2 with inverse contrast: ( x x ) protonated laurate and (0 0) deuterated laurate adsorbed onto 222 A latex particles.D. CEBULA, R . K . THOMAS, N. M. HARRIS, J . TABONY, J . w. WHITE 87 sity distribution with respect to the mean [eqn (7)]. The observed difference in sign of the slopes is due to the deuterated and protonated laurate layer having higher and lower scattering length densities than the mean, respectively. With the available data, (4 and 3 points), these slopes cannot be evaluated to greater accuracy than -(4.2 & 1.4) x 1013 (protoiiated case), and (9.0 5 3.3) x 1013 (deuterated case), c.f. -3.2 x 1013 and 7.0 x loi3 as calculated from the layer thickness and density as measured.It should be stressed that the measurements made on these adsorbate systems were done with a few hours measuring time. It is clear that much greater precision is available, not only from a increased counting time, but also from an improvement in the design of the experiment profiting from what has been learnt during the test series. THE CARBON SOLS The effects of polydispersity on the small angle neutron scattering pattern can be readily seen in fig. 7 where the (In& Q2) plots for 2% by weight of Vulcan I11 are dis- persed in various H20 + D20 mixtures is shown. The curves do not show Guinier behaviour but it is evident that contrast matching occurs as the D20 concentration 7 6 5 0 O 0 0 0 100 200 300 400 500 (momentum transfer)' I IO-~A-* FIG.7.-Variation of the small angle scattering pattern from a 2% weight for weight colloid of Vulcan 111 graphite particles in H20 + D20 mixtures. m, 0% D20; a, 30% DzO; a, 50% D20; 0,80% DzO; A, 100% DzO; 0, background 100% HzO. varies. For the purposes of characterising the sol, and apparent radius of gyration, and an extrapolated intensity at I(0) may be obtained, using the approximately linear region above 200 + A-2. The parameters determined by this method at various contrasts are listed in table 3. In all cases the curves were corrected for sample self absorption. The square root of the intensity at zero angle is plotted as a function of the solvent scattering length density in fig. 8, where it can be seen that a reasonably good straight line is obtained leading to a mean scattering length density for the carbon particles of (6.65 & 0.7) x 1O1O cm-2.This value leads immediately to a value for the density of the carbon particles of 2.0 & 0.2 g cm3 by comparison with literature values88 NEUTRON SCATTERING FROM COLLOIDS TABLE 3.-cONTRAST VARIATION PARAMETERS FOR VULCAN III CARBON DISPERSED IN H20/D20 MIXTURES. 0 396 5.98 19.9 402 30 1 64 5.10 12.8 391 50 101 4.61 10.0 402 80 21.8 3.08 4.7 402 - 100 1.8 0.59 1.3 Intensities corrected for self absorption and normalised to 2.5 x lo5 monitor counts ~~ ~~~ ~ between 1.9 and 2.6 g cm3 for graphite and 2.2. g calculated from crystallo- graphic data on crystallite graphite. A determination of this kind can be a quick check on the microporosity and density of colloidal materials; the experiment can be done in a matter of an hour or two.When sodium dodecyl sulphonate is adsorbed on the carbon particles, a marked change in the mean scattering length density of the particles can be noted in the same way as has been demonstrated for the polystyrene latex particles. volume % D,O 2 5 -1 0 1 2 3 4 5 6 7 8 scattering length density / 10’3crn-2 FIG. 8.-Dependence of the square root of the scattering intensity at zero angle as a function of the scattering length density of the surrounding solvent for 2% weight for weight Vulcan 111 in H20 + D20. MONTMORILLONITE SOLS Because montmorillonite sols typically have a platelet thickness (H) of about 10 A and a platelet extension (3) of about 2000 A, it is possible by choosing the range of momentum transfer observed in a neutron small angle scattering experiment to study selectively adsorption and clustering phenomena on the surface of the platelets.These measurements are naturally made at much large momentum transfers than those for studying particles of diameter -2OOA. Fig. 9 shows the small angle neutron scattering for a 1 % weight for weight solutionD . CEBULA, R. K . THOMAS, N . M . HARRIS, J . TABONY, J . w. WHITE 89 of lithium montmorillonite in water corrected for background and detector efficiency. The linear section of the curve is well represented by 1 I(Q) cc p exp (-Q2H2/12) where H has the value of 10.3 A. This is a clear indication that the lithium mont- morillonite system is well dispersed.0.002 0.006 0.010 &;1-? FIG. 9.-Small angle neutron scattering from a 1% weight for weight solution of lithium montmoril- lonite in water corrected for background and detector efficiency. By contrast, as the counter ion is changed to sodium through potassium to caesium, there is a marked change in the small angle scattering pattern and, in the case of the caesium sol with the same concentration of montmorillonite, there is a marked tend- ency to follow a Q-4 law (fig. 10). Only at the lowest momentum transfers is there a tendency for the curve to turn round to follow a Q - 2 law; this sets an upper limit on the particle thickness, H, of around 40 A. The potassium montmorillonite sols can be represented in the same way as caesium, but the scattering from the sodium case is unusual and is not well represented by any of the approximate forms for I(Q) given in the Introduction.Insofar as it has been possible to detect clustering of platelets of caesium mont- morillonite, it is evident that the study of adsorption on the platelets is readily acces- sible through low angle neutron scattering; the platelet surface area is of the order of 800 m2 8-l and the contrast matching point for the montmorillonite mineral lies between 60 and 70% D20, depending on whether a full proton exchange or no proton exchange with the protons in the mineral occurs. GENERAL DISCUSSION The experiments reported here were designed to test the efficacy of neutron small angle scattering for determining the structure of the adsorbed phases on colloidal particles in liquid dispersion.For monodispersed systems like the polystyrene latex, the precision of the measurements is only limited by the measurement times, and could90 NEUTRON SCATTERING FROM COLLOIDS I 102 0 1%’ 10’ FIG. 10. Small angle scattering from a 1% weight for weight solution of caesium montmorillonite in water corrected for background and detector efficiency. The slope of the log-log plot is -4 indicating that aggregation of the particles has occurred. be improved to of the order of 1 A for the surface layer thickness, with extended measurement times on each sample to of the order of an hour or two. In the case of polydispersed articles, information on the mean particle density with and without adsorbant can be obtained readily, though further work needs to be done to set the limits on precision introduced by the effects of polydispersity. Even for such systems, the neutron small angle scattering method may be of value, in characterising the colloidal dispersion in the size range 10-500 A, so our measure- ments over a large momentum transfer range models for the particle size distribution can be fitted from the scattering curves. The measurements reported here concern only simple adsorbates. It is clear that for larger particles in using contrast matching of the adsorbent, small angle scattering patterns from adsorbed polymeric species and other stabilising agents could well be determined for dilute solutions in a manner entirely analogous to the isotropic sub- stitution method used for determining polymer concentrations in the bulk and in so1ution.12* l3 These experiments were conceived in discussions with Prof. R. Ottewill, whose help is hereby acknowledged. W. Schmatz, T. Springer, J. Schelten and K. Ibel, J. Appl. Crysf., 1974, 7, 96. B. Jacrot, Rep. Prog. Phys., 1976, 39, 911-953. A. Guinier, Ann. Phys., 1939, 12, 161-237. H. B. Stuhrmann, Actu Cryst., 1970, A26, 297.D . CEBULA, R . K . THOMAS, N. M . HARRIS, J . TABONY, J . W. WHITE 91 J. C. Brown, J. W. Goodwin, R. H. Ottewill and P. M. Pusey, Colloid and Interface Science. Hydrosols and Rheology, ed. M. Kerker (Academic Press, 1976), vol. 4. P. Connor, Ph.D. Thesis (University of Bristol, 1968). D. H. Everett, G. D. Pafit, K. S. W. Sing and R. Wilson, J. AppZ. Chem. Biotechnol., 1974, 24, 199. R. H. Ottewill, personal communication. lo I. C. Callaghan and R. H. Ottewill, Faraday Disc. Chem. SOC., 1974, no. 57. l1 R. H. Ottewill, personal communication. l2 H. Benoit, D. Decker, J. S. Higgins, C. Picot, J. P. Cotton, B. Farnoux, J. Jannink and R. Aubert, Nature, Phys. Sci., 1973, 245, 13. l3 G. D. Wignall, D. G. H. Ballard and J. Schelten, Eur. PoZymer J., 1975, 10, 861. ’ A. I. Medalia and F. A. Heckman, Carbon, 1969,7, 567.

ISSN:0301-7249    

DOI:10.1039/DC9786500076

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Statistical Mechanical Approach to Phase Transitions in Colloids BY WILLIAM VAN MEGEN AND IAN SNOOK Department of Applied Physics, Royal Melbourne Institute of Technology, Melbourne, Victoria, Australia Received 6th December, 1977 The Monte Carlo method and a number of approximate theories, based on classical statistical mechanics and using DLVO pair potentials, are used to calculate the structure and the osmotic pressure of electrostatically stabilized dispersions of spherical particles. Reasonable agreement is found between the exact Monte Carlo radial distribution functions and the corresponding quantity determined from the hard sphere model. This hard sphere model provides a simple unifying theory for the structure of these colloidal solutions provided that the equivalent hard sphere diameter is chosen correctly.From the good agreement between experiment and these and previous calculations, we conclude that the DLVO pair potentials are adequate to calculate at least the structure of colloidal solutions. 1. INTRODUCTION Many works have illustrated the usefulness of and the necessity for using statistical mechanics to determine the properties of colloidal solutions [see, for example, ref. (1)-(6)]. These ideas have more recently been applied to a variety of dispersions of spherical and non-spherical particles to calculate, in particular, the conditions for the separation of a phase of regularly arranged particle^.^*"^ In all cases, such calcula- tions have reproduced at least the qualitative features of real colloidal systems.It is the aim of this discussion to examine more closely the structure of colloidal solutions and its dependence on volume fraction and temperature and electrolyte concentration of the suspending medium. Considerable emphasis has been placed on very dilute systems of small particles for which the structure is quantitatively accessible experi- mentally. 9*10 Since the application of statistical mechanics to a many-particle system presupposes the knowledge of the potential energy of the system due to the interactions among the particles," we briefly examine the assumptions on which the usual interaction poten- tials for colloidal particles (uiz. those formulated in the DLVO theory)12 are based. Statistical mechanics explicitly applied to a system with a large number of particles is exact for given interaction potentials among the particles.Hence, any discrepancy between the results of exact statistical mechanical calculations and experiments on corresponding systems can only arise from inadequacies in the formulation of inter- action potentials. To be specific we restrict the following discussion to an electrostatically stabilized dispersion of identical solid spheres in an aqueous electrolyte. In the usual formula- tion the total interaction energy, U, between two colloidal particles of separation rtJ, is regarded as the sum of the van der Waals attraction, U,, plus the double layer repulsion, V, : l2 W , j > = U*(P'ij> + U&>. (1.1)W. VAN MEGEN AND I . SNOOK 93 In the absence of external fields and assuming pairwise additivity, the total excess1 potential energy is given by @ = 2 U(rij).i < j Since the double layer repulsion dominates in most of the situations discussed below, it may be worthwhile examining the implication of the assumption expressed by eqn (1. I) and (1.2) for this contribution. The double layer repulsion is essentially coulomb repulsion, due to the net charge on the particles, screened by the intervening electrolyte. The magnitude of this screening depends on the charge and distribution of the ions in the background medium; to determine this exactly in a colloidal solution is an immensely complex problem. The assumption of pairwise additivity simplifies this problem considerably by assuming that the distribution of ions in the vicinity of an isolated pair of charged colloidal particles remains unperturbed by the approach of a third particle. This assumption may appear somewhat drastic particularly in moderately concentrated dispersions in which the double layers overlap.It must be emphasized, however, that many properties, such as the occurrence of a disorder to order (D-0) transition, are not critically dependent on the inclusion of many-particle potentials nor on the precise details of the pair potential? This statement is clearly substantiated by the excellent overall agreement between experiment and statistical mechanical calculations, based on simple phenomenological pair potentials, for both molecular systems l1 and colloidal s o l ~ t i o n s . ~ ~ * ~ ~ Calculations using simple asymp- totic forms for both the van der Waals attraction and the double layer repulsion have yielded structure factors l3 and osmotic pressures l4 in quantitative agreement with corresponding experimental values for monodisperse polystyrene latexes.Further, since the pressure is very much more sensitive to the precise form of the interaction potential, the reasonable agreement between the calculated and measured osmotic pressures in concentrated dispersions illustrates that the effect of three or more particle potentials is not large under the conditions studied so far, and that the pair potentials formulated in the DLVO theory should certainly be adequate for determination of the structure. The structure of a many particle system is quantitatively given by the radial distri- bution function, which is of further interest since it provides a vehicle for relating the pair potential to excess equilibrium properties.ll Analogously, the time-dependent distribution function, or the van Hove space-time correlation function provides the key to the dynamic ~r0perties.l~ Both distribution functions are accessible by auto- correlation of the intensity of laser light scattered from suspensions.Examination of the radial distribution function tells us whether the suspension is ordered or dis- ordered. It is this ordering or regular stacking of the particles which gives rise to the familiar iridescence observed in concentrated polystyrene latexes. In the next section we outline the essential statistical mechanics and the main ideas underlying the numerical procedure (Monte Carlo method) for evaluating the multidimensional integrals.The one drawback of this direct procedure is the enormous amount of computing time required to locate precisely a phase transition (the D-0 transition in this case). It is, therefore, useful to use a combination of a number of approximate methods, such as the cell model and perturbation theory, to locate the D-0 transition more e~pediently.~ The simplest approximate approach is the hard-sphere model which exploits the fact that the structure in dense systems, and in particular the occurrence of a D-0 transition, is essentially a packing phenomenon arising from the effective size of the particles, i.e., the actual size of the particles plus an allowance for the strongly repulsive part of the pair potential.8*16 These approxi- mate methods are also briefly reviewed in section 2.In section 3 results are presented94 PHASE TRANSITIONS I N COLLOIDS for dispersions in which the double layer thicknesses are small and large, respectively, compared with the partick radius. 2. THEORETICAL In the usual formulation of classical equilibrium statistical mechanics the radial distribution function, g(r), and the pressure, P, for an isotropic system of spherical particles are given by and in which N is the number of particles in volume V, k is the Boltzmann constant, T is the absolute temperature and N(r, r + 6r) is the number of particles within a distance r, r + 6r from a given particle.ll The pair potential U(rij) is given by eqn (1 .l) with12 UR(rlj) = 2neoeryi ln(1 + exp(-icauij), lca $ 1 (2.4) in which uij = (rij/a) - 2 is the surface to surface separation in units of the particle radius a, K is given by IC = (ST)% and all other symbols have their usual meaning.12 The angular brackets in eqn (2.1) and (2.2) represent averages over the canonical (or N, V, T ) ensemble; in the Monte Carlo (MC) method of Metropolis et a1.l’ these are explicitly evaluated by a numerical technique. For practical reasons the real system containing a very large number of particles is replaced by a periodic system.Each cell of this periodic system contains a small number (up to 108 for the present computations) of particles which are allowed to interact among themselves and also with their periodic images. This restriction does not introduce any significant error provided the range of the correlation between the particles is smaller than the length of the unit cell.Considerable difficulty arises in the vicinity of a phase transition (such as the D-0 transition) where the small number of particles is inadequate to examine two phases in equilibrium.ll It is still possible, however, to locate the volume fraction at which the disordered phase begins to order (qD) and that at which the ordered phase disorders (q0) by using an indirect approach discussed, for example, by Hoover and Reel8 to locate the melting transition in molecular solids. In this approach one constructs a reversible thermodynamic (P,q) curve connecting the ordered and disordered phases by using a single occupancy model to localize the particles and thus stabilize the ordered phase at low volume fractions.The excess free energies are determined by integrating the pressure curves of the disordered and artificially ordered systems. Subsequent equating of the Gibbs free energy and pressure for each phase locates pD and qo.W . VAN MEGEN AND I . SNOOK 95 Since the above procedure is tedious and requires comparatively large amounts of computer time it is extremely useful to develop simpler, albeit approximate, methods for evaluating the properties of many-particle systems. Unlike the MC method, these approximate techniques are only likely to be applicable under certain restricted conditions. Two very successful approximate theories are the hard-sphere perturba- tion theory (for disordered or fluid-like phases)ll and the cell model (for ordered or crystal-like phases).7* l9 Briefly, in perturbation theory7*11 the pair potential is divided into a steep, repul- sive reference part U, and a longer ranged, weaker perturbation, Up, i.e., u = u, + up.(2.7) A given thermodynamic property can then be written as a perturbation series, ex- panded about the property of the reference system, i.e., the system of particles with the pair potential U,. For example, the Helmholtz free energy A and the radial distribu- tion function, g(r), are ----+J+>+...., A - A0 A A NkT NkT NkT NkT and It is, of course, particularly useful to relate A. and go(r) to a system of hard spheres since the properties of this system are already known very accurately.For a given system (pair potential) the central problem is then to carry out suitably the division expressed in eqn (2.7) and choose an appropriate equivalent hard sphere to replace U,. This in general depends on a number of factors such as the range and softness of the pair potential, the density and the temperature.ll One method for dividing up the pair potential is given in the Barker-Henderson (BH) theory11*20 in which one writes g(r) = go@) + gl09 + * * * * * (2.9) and u, = u = o up = 0 = u r S p r > p r L P (2.10) r > p and the break point 11 is chosen so that U, is a harsh repulsive (hard-sphere like) potential and Up is a weaker slowly varying potential. The effective hard sphere diameter is given by d = /om [exp(- U,/kT) - lldr. (2.1 1) With this criterion both go and g, are usually required to obtain a good approximation for g(r). The Chandler-Weeks-Anderson (CWA) theory 11s21 presents a second method in which the pair potential is broken up as follows : and u,=u+c Up = -& = o = u (2.12) where U(p) = --e and p and d are chosen to produce a hard sphere diameter so that go(r) is as close as possible to g(r).This is achieved by making the difference between A . and Ahs zero to first order. Both the above theories give essentially equivalent results for simple liquids .I1 9 2o 2196 PHASE TRANSITIONS IN COLLOIDS In the cell model one replaces the array of particles by a regular array of potential cells which constrain the motion of each parti~1e.l~ This leads to the following expression for the canonical partition function 2; (2.13) where Eo is the static lattice energy, vf is the free volume available to each particle and all other symbols have their usual meaning. In the “ sphericallized ” or “ smeared out ” approximation, vf becomes vf = 4n r2 exp( - [ ~ ( r ) - y(O)]/kT} dr, (2.14) where C is the effective cell radius and y(r) is the particle potential energy when displaced a distance r from the cell centre.6 3. RESULTS AND DISCUSSIONS To illustrate the quantitative difference between ordered and disordered colloidal solutions, fig. 1 shows g(r) as determined by the MC method for a dispersion of spheres of radius a = 5.95 x loA7 m in a 1-1 electrolyte of concentration c = 0.1 mol m-3. For this system the pair potential is comparatively hard and short ranged [i.e., K a B 1 and we use U, given in eqn (2.4)], as opposed to systems to be discussed r l r FIG.1 .-Radial distribution function g ( r ) plotted against r in units of the particle diameter CT showing MC (-) and hard sphere (- - - -) results; (a) rp = 15%, (b) v, = 25%, (c) v, = 35%. later, for which the pair potential is soft and long ranged (rca < 1). For q of 15% and 25%, g(r) is qualitatively similar to that of a simple liquid, indicating a disordered arrangement of particles, whereas for q = 35%, g(r) indicates a long ranged crystal- like behaviour. Fig. 1 also shows the hard sphere perturbation results obtained using CWA theory (the BH results being almost identical). The hard sphere diameter is roughly at the point where U = 1 kT. Fig.2 shows Pa3/kT plotted against q, as determined by first order perturbation theory for q < q,, and the cell model for q 2 qo, for various concentrations, c, of the background electrolyte. The accuracy of these methods, by comparison with MC results, has been established in earlier work.’ Note that as c decreases so does the volume fraction pD at which the ordered phase begins to separate from the disorderedW. VAN MEGEN AND I. SNOOK 97 phase, as does the difference between qo and pD. Both these predictions are in accord with experimental observation.22 It is also interesting to note the maximum in the osmotic pressure at the D-0 transition as c is varied from 1 to mol m-3. As discussed in previous work, considerable difficulty arose in using the cell model and first order perturbation theory to locate the D-0 transition for systems in which the attractive tail in the pair potential is significant.14 In the case of c = 1 mol m-3 the depth of the secondary minimum # 1 % FIG.2.-Osmotic pressure Pa3/kT plotted against q, around the D-0 transition, for various electro- lyte concentrations; (a) c = 1 mol mW3, (b) c = 0.5 rnol mW3, (c) c = 0.1 rnol m-3, ( d ) c = 0.05 mol M-~, ( e ) c = 0.01 mol m-3. MC result indicated by *. in U is about 1 kT rendering an error in qD and qo of M 1 % in q and possibly an over- estimate of one (SI) unit in Pa3/kT. For the system under examination here, the primary maximum in the pair potential is of the order of lo3 kT and, for interparticle spacings beyond this, the effect of the van der Waals attraction is negligible compared with the double layer repulsion.At least for c < 0.5 mol m-3 the secondary minimum is less than ~ 0 . 1 kT. Thus, as c is decreased below 0.5 mol m-3 U, becomes not only longer ranged, accounting for the reduction of qD and qo, but also less steep or softer. Since the pressure is essentially the ensemble average of the gradient of the pair potential averaged over all pairs of particles in the system, the increase in the osmotic pressure at the D-0 transition can be attributed to the steepening of the pair potential with increasing electrolyte concentration. However, for c > 0.5 mol m-3 the appearance of a comparatively small secondary minimum (1 kT at c = 1 mol m-3) in the pair potential causes a sudden drop in the pressure at the phase transition.That this reduction in the osmotic pressure stems from the secondary minimum is easily confirmed by comparing the pressures, at the estimated qD (or qo), determined by the hard sphere method,8 which allows only for the positive part of the potential, and first order perturbation theory, which approximately allows for the negative tail in the pair potentials; these pressures are 2.7 x and 1.4 x N m-2, res- pectively. Interestingly, a similar effect has recently been observed by Takano and ha chis^^^ in an experimental determination of qD and qo for polystyrene latex in several concentrated electrolytes. This experiment then presents further experimental verification of the secondary minimum in electrostatically stabilized colloids.Also included in fig. 2 are the results of a complete MC determination of qo and qD for c = 0.1 mol m-3 using the approach of Hoover and Ree.18 Clearly the approximate methods, although not exact, provide a reasonable and expedient estimate of yo and qD. We turn now to systems for which the pair potential is very soft and long ranged98 PHASE TRANSITIONS I N COLLOIDS [ K a < 1, and we use eqn (2.5) for U,]. This occurs in dispersions of very small particles in dilute electrolytes. These systems are particularly attractive since g(r) can be determined experimentally by means of laser light scattering. In more concentrated dispersions of larger particles such experiments are plagued by multiple scattering effects. The effect of temperature on the structure of a system of spherical particles, a = 4.36 x m, in a monovalent electrolyte, c = 2.9 x low3 mol m-3, was recently carried out by Schaefer.1° In fig.3 we show the MC determination of 3 I FIG. 3.-Radial distribution functiong(r) plotted against r for a = 4.36 x lo-* m and c = 2.9 x 10 niol m-3, showing MC (-----) and hard sphere (- - - -) results, Q = 2a. g(r) and the BH result (go + g,) for this system. It should be noted that in this case U(d) N 7 kT and d is strongly dependent on y. Fig. 4 compares the calculated structure factor, S(K), with that measured by SchaeferlO at a temperature of 46 "C. The structure factor is related to g(r) by S(K) = 1 + - - l ] r sinKrdr, where 4nn 2. K = - sin (012) 2 1 :: 0 4 08 12 16 2 0 2 A Kb FIG. 4.-Structure factor S(K) as a function of the magnitude of the scattering vector, K, in units of the reciprocal diameter, showing MC (-) and experimental (.) results.is the magnitude of the scattering vector, 8 is the scattering angle, il is the wavelength of the scattered radiation and n is the refractive index of the medium. The agreemint is quite reasonable considering the simplicity of the interaction potential used and the expected errors in such measurement^.^ Schaefer also measured the effect of tem- perature on S(K) and found that this quantity indicates virtually no structure at 70 "C and a very pronounced structure at 40 "C (with freezing occurring at 39.5 "C). In direct contrast, our MC computations between 40 and 70 "C indicate no significant variation in S(K). The calculations assume the surface charge to remain constant,W.VAN MEGEN AND I . SNOOK 99 in which case the surface potential yo increases with increasing temperature. The resulting increase in the repulsion compensates the reduction in structure due to the Boltzmann term. The observed disappearance of the structure with temperature is readily accounted for by assuming some degradation of the ion exchange resin with the consequential increase in concentration of background electrolyte. The dramatic effect of this is shown in fig. 5 where the g(r) values are reduced to dilute gas-like shapes n L U br 2 6 0 10 12 14 r / 0, FIG. 5.-Radial distribution functions for a = 4.36 x lo-' m and c = mol m-3 (-----) and c = 2.9 x mol m-3 (- - - -). when the electrolyte concentration is increased to and 2.9 x mol m-3.Indeed, Schaefer mentions that his ion exchange resin degrades irreversibly above 60 "C. We are at a loss, however, to account for Schaefer's observation of the large increase in the magnitude of the first peak in S(K) upon decreasing the temperature below 46 "C. The only explanation we can offer is that the discrepancy may be due to experimental errors or the inadequacy in the formulation of the potential energy (or both). 4. CONCLUSIONS From the preceding discussion it is evident that the structure of monodisperse systems of spherical particles is adequately explained by statistical mechanical calcula- tions based on pair potentials given in the DLVO theory. It has also been shown that g(r) is reasonably predicted by a hard sphere approach.Considerable care must be exercised in selecting the correct hard-sphere diameter particularly for very long ranged potentials. The results are clearly very sensitive to variations in the hard sphere diameter; arbitrarily setting this at a point where the pair potential has decayed to E 1 kTis by no means sufficient. It is essential that all the parameters characteriz- ing the system are accurately known. The sensitivity of the calculated results to the surface potential, yo, has been discussed in earlier worki3 whilst the drastic variation of g(r) with electrolyte concentration has been illustrated above. The above results also indicate that the structure of colloids is insensitive to temperature variations, provided that the particle surface charge and the electrolyte concentration do not vary with temperature.L. Onsager, Ann. N.Y. Acad. Sci., 1949, 51, 627. I. Snook and W. van Megen, Colloid and Interface Sci., ed. M. Kerker (Academic Press, N.Y., 1976), vol. IVY p. 1. R. P. Keavey and P. Richmond, J.C.S. Furaday 11, 1976,72, 773. S. Marcelja, D. J. Mitchell and B. W. Ninham, Chem. Phys. Letters, 1976, 43, 353. W. G. M. Agterof, J. A. J. van Zomeren and A. Vrij, Chem. Phys. Letters, 1976, 43, 363. S. L. Brenner, J. Phys. Chem., 1976, 80, 1473. W. van Megen and I. Snook, J. Colloid Inlerface Sci., 1976, 57, 40, 47.100 PHASE TRANSITIONS I N COLLOIDS W. van Megen and I. Snook, Chem. Phys. Letters, 1975, 35, 399. J. C. Brown, P. N. Pusey, J. W. Goodwin and R. H. Ottewill, J. Phys. A , 1975, 8, 664. lo D. W. Schaefer, J. Chem. Phys., 1977,66, 3980. l1 J. A. Barker and D. Henderson, Rev. Mod. Phys., 1976,48, 587. l2 E. J. W. Verwey and J. Th. G. Overbeek, Theory of stability of Lyophobic Colloids (Elsevier, l3 W. van Megen and I. Snook, J. Chem. Phys., 1977,66, 813. l4 A. Homola, I. Snook and W. van Megen, J. Colloid Interface Sci., 1977, 61, 493. l5 S. H. Chen, Physical Chemistry, An Advanced Treatise, ed. H. Eyring, D. Henderson and W. l6 P. Jena and W. R. Smith, Chem. Phys. Letters, 1973, 21, 295. l7 N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. l8 W. G. Hoover and F. H. Ree, J . Chem. Phys., 1967, 47,4873. l9 J. A. Barker, Lattice Theories of the Liquid State (Pergamon, Oxford, 1963). 2o J. A. Barker and D. Henderson, J. Chem. Phys., 1967, 47, 2856,4714; Accounts Chem. Res., 21 H. C. Andersen, D, Chandler and J. D. Weeks, Phys. Rev. A , 1971, 4, 1597; J. Chem. Phys., 22 S. Hachisu and Y . Kobayashi, J. Collaid Interface Sci., 1973, 42, 342. 23 K. Takano and S . Hachisu, J. Phys. SOC. Japan, 1977, 42, 1775. Amsterdam, 1948). Jost (Academic Press, N.Y., 1971), vol. VIIIA. Phys., 1953,21, 1087 1971,4, 303; Phys. Rev. A , 1971,4, 806. 1972,56, 3812.

ISSN:0301-7249    

DOI:10.1039/DC9786500092

出版商:RSC    

年代:1978

数据来源: RSC